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WORKS OF 
PROFESSOR CECIL H. PEABODY 

PUBLISHED BY 

JOHN WILEY & SONS. 



Thermodynamics of the Steam=engine and other 
Heat-engines. 

This work is intended for the use of students ii 
technical schools, and gives the theoretical training 
required by engineers. 8vo, cloth, $5.01 

Tables of the Properties of Saturated Steam and 
other Vapors. 

These tables were prepared for the use of students 
1 technical schools and colleges, and of e 
general, svo, cloth, $1 00. 

Valve=gears for Steatn=engines. 

This book is intended to give engineering students 
valve-g-ears for steam-engines. Second Edit:' 
vised and Enlarged. Svo, clotn, $2.50. 

Steam=boilers. 

By Prof. Cecil H. Peabody and Prof. Edward 
F. Miller, Nearly 400 pages; 142 illustrations. 8VO, 
cloth, $4.00. 

Manual «. the Steam=engin< 

154 pages; 98 figures. 1211 

Naval Architecture. 

v+616 pages; 217 figures. £ 



Indicator. 

o, cloth, $1.50. 



VALVE-GEARS 

FOR 



STEAM-ENGINES 



CECIL H. PEABODY 

Professor of Naval Architecture and Marine Engineering 
Massachusetts Institute of Technology 



SECOND EDITION, REVISED 
FIRST THOUSAND 



NEW YORK 

JOHN WILEY & SONS 

London : CHAPMAN & HALL, Limited 

1906 






LIBRARY of CONGRESS 
Two Cooies Received 

FEB 23 .906 

^Copyright Entry 
CLASS CL* XXc, No. 

/ 3 E & & & 

/ ^ COPY B. 



Copyright, 1890, 1906 



CECIL H. PEABODY 



ROBERT DRUMMOND, PRINTER, 



: 



PREFACE. 



This book is intended to give engineering students instruc- 
tion in the theory and practice of designing valve-gears for steam- 
engines. With the vast number of valves and gears in use at 
the present time, an exhaustive treatment in a text-book appears 
out of place; the author's aim is rather to give the learner a 
firm grasp of the principles and some facility in their application. 
Each type discussed is illustrated by one or more examples selected 
from good practice. 

Graphical methods are used throughout, in the body of the 
book, both for demonstration of principles and for design of 
gear. In an appendix analytical demonstrations are given of 
certain principles that cannot be treated in a complete and 
satisfactory manner by construction only. Zeuner's valve-diagram 
is used because it is widely and favorably known and appears to 
the author to be at least as good as any other circular diagram. 

In the discussion of radial valve-gears, the underlying prin- 
ciples found in all such gears are pointed out, and a few prominent 
forms are illustrated. All such gears have necessarily or designedly 
large irregularities in their motions, so that analytical methods 
are useless if not misleading, and general methods of treatment 
are of small value. Facility in design is to be obtained through 
experience only. 

Drop cut-off gears are represented by a few examples chosen 



VALVE-GEARS FOR STEAM-ENGINES. 



CHAPTER I. 
PLAIN SLIDE-VALVE. 

The valve-gear of a steam-engine consists of the valve, or 
valves, for admitting steam to, and exhausting steam from, the 
cylinder of the engine, together with the mechanism for giving 
motion to the valve, or valves. The discussion of valve-gears 
is therefore a part of kinematics or mechanism; the extent and 
importance of the subject make a separate presentation of it 
desirable. 

The larger part of valve-gears derive their motion from one 
or more eccentrics; of such gears, the plain slide-valve is the 
simplest. Other valve-gearS are best studied after an exami- 
nation of the plain slide-valve, since they accomplish the same 
results, and by analogous methods. 

Slide-valve Engine. — A plain slide-valve engine has two 
trains or systems of moving parts, the piston, piston-rod, con- 
necting-rod and crank, and the eccentric, eccentric-rod, valve- 
spindle and valve. These parts are represented in Figs, i, 2 
and 3 of Plate I; the engine-frame is omitted from the figures 
to simplify them and to concentrate attention on the moving 
parts, in which we are now interested. 

The piston, half of which is represented in Fig. 2, is sub- 
jected to steam pressure on its right-hand side and presses the 



2 VALVE-GEARS FOR STEAM-ENGINES. 

piston-rod toward the left. The piston-rod is joined to a cross- 
head H (partly obscured by the valve-spindle), which moves in 
straight guides. The right-line reciprocating motion of the cross- 
head is transformed into a rotating motion by the connecting-rod 
L, which takes hold of the crank-pin C. At O is the centre of the 
engine-shaft, to which are keyed the crank OC and the eccentric E. 
The eccentric-rod / transforms the rotating motion of the eccentric 
E into the reciprocating motion of the head h of the valve-spindle, 
and the valve-spindle communicates that motion to the valve V. 
The valve is in this case placed at the side of the cylinder be- 
cause the side-elevation brings the centre-lines of the moving 
parts into a simple relation, shown by Fig. 4, and this represen- 
tation of the problem will be considered to be the normal case 
to which all other cases are assimilated, whatever variations may 
be found in actual practice. In the side-elevation, Fig. 1, the 
valve-chest cover is removed to show the valve, and the upper 
part of the valve is represented to be cut away to show the steam- 
passages. 

Fig. 2 gives a horizontal section of the half cylinder, steam- 
passages, valve and valve-chest. In the design of a plain slide- 
valve it is customary to represent it in section, as in Fig. 3, which 
is drawn to a larger scale, with the valve in its middle position. 

Crank and Connecting-rod. — The crank, connecting-rod and 
cross-head, in its guides, form a train of mechanism known as 
a sliding-block linkage. In Fig. 4, OC is the centre-line of the 
crank and CH is that of the connecting-rod; the point H is con- 
strained to move on the line OX. 

In designing valve-gears two problems may arise in the train 
made up of the crank, connecting-rod and cross-head, with its 
attached parts, the piston and piston-rod. They are (1) given 
the piston-displacement to find the crank-angle; and, conversely, 
(2) given the crank-angle to find the piston-displacement. Both 
are habitually solved graphically. In Fig. 4 first find the begin- 
ning of the stroke of the cross-head by laying off OA equal to 



PLAIN SLIDE- VA LVE. 3 

the length of the crank plus the length of the connecting-rod. 
From A lay off All equal to the piston-displacement. With A as a 
centre and with a radius equal to the length of the connecting-rod, 
draw an arc cutting the circular path of the centre of the crank- 
pin at C; then CO A is the crank-angle. Conversely, lay off 
the crank- angle AOC, and, with C as a centre and the length of 
the connecting-rod as a radius, intersect the path of the cross- 
head at H; then AH is the displacement of the cross-head 
and the piston. The centre-line of the cylinder is intended to 
pass through the centre of the shaft; small deviations are com- 
monly ignored. 

Eccentric and Eccentric-rod. — The eccentric is derived 
from the crank by the expansion of the crank-pin till it includes 
the shaft and obliterates the crank. Consequently the eccentric 
and eccentric-rod form sliding-block linkage. 

The length of the eccentric-rod is commonly from 12 to 20 
times the eccentricity, and the deviation of the true motion from 
harmonic motion is small and can usually be neglected. Should 
it be desirable in any case, the true motion can be determined 
graphically by the method given for the crank and connecting- 
rod. 

Problems in valve-gears are solved by special methods to be 
described later; a solution of such problems involving an exten- 
sion of the graphical method of page 2 will be given on page 5 
in connection with the valve-ellipse. 

The Slide-valve. — Fig. 3 gives the section of a plain slide- 
valve and its seat. The ports a, a x lead to the two ends of the 
cylinder; the exhaust- space s is connected with the exhaust- 
pipe; the bridges b, &i separate the ports from the exhaust-space. 
The steam-pressure in the steam-chest holds the valve against 
the seat and prevents leakage. The valve-seat is cut away so 
that the valve may over-travel its seat at the ends and thus both 
valve and seat may wear evenly. The edges of the ports and 
of the valves are machined and finished true; for convenience 



4 VALVE-GEARS FOR STEAM-ENGINES. 

in the work, the edges of the ports and the inside edges of the 
valve are undercut as shown. 

The valve, when in its mid position, commonly overlaps both 
inside and outside edges of the ports. The amount, o, by which 
it laps over the outside edge of the port is called the steam-lap 
of the valve; the amount, i, by which it laps over the inside 
edge of the port is called the exhaust-lap. In the typical case 
represented by Fig. 3 the valve is exposed to the steam-pressure 
on the outside, and the exhaust-cavity and the exhaust-port are 
inside; in some cases this arrangement is reversed. In any case 
the steam-lap is the distance that the valve must be moved from 
middle position to let steam into the cylinder, and the exhaust- 
lap is the distance it must be moved to open the port to exhaust. 
The exhaust-lap may be nothing or negative. In the latter case 
the valve is said to have a clearance. 

In Fig. 2 the valve is shown admitting steam to the end of 
the cylinder remote from the crank, called the head end; and it 
is exhausting steam from the other end of the cylinder, called the 
crank end. The valve is usually set in such a manner that when 
the engine is on a dead-point the valve is open by a small amount 
called the lead. For this purpose the eccentric is set ahead of 
the crank 90 plus the angle 0, called the angular advance. This 
definition applies only to the typical case represented by Fig. 4; 
a more general definition will be given later. As the crank moves 
forward the valve opens more and more till the centre of the 
eccentric comes to the line of centres, then the valve begins to return 
and it shuts the port before the stroke of the piston is finished. 
The stroke of the piston from the head end to the crank end of the 
cylinder is called the forward stroke; the return stroke is made from 
the crank end to the head end. The valve is open by the amount of 
the lead at the beginning of the return stroke, and at the same time 
the exhaust is open for the head end. As in the forward stroke, the 
valve first opens wider as the stroke proceeds, then it returns and 
closes the port before the piston reaches the end of the stroke. 



PLAIN SLIDE-VALVE. 5 

Events of the Stroke. — When the outside edge of the valve 
is at the edge of the port, as shown by Fig. 4, PI. II, and the 
valve is opening, admission is said to occur. This happens just 
before the stroke commences. When the valve is in the same 
position, but is closing, cut-off takes place. At either position 
the displacement of the valve is equal to the steam lap; con- 
sequently we have the following principle: 

When the displacement of the valve is equal to the steam lap, 
the engine is either at admission or cut-off. 

Release occurs when the inside edge of the valve is at the 
edge of the port and the valve is opening to exhaust, as shown 
by Fig. 5, PI. II. 

Compression occurs when the valve is at the same position 
but is closing the exhaust. At either position the displace- 
ment of the valve is equal to the exhaust lap ; consequently we 
have: 

When the displacement of the valve is equal to the exhaust lap, 
the engine is either at release or at compression. 

Valve-ellipse. — The following method will be found con- 
venient for studying the action of a valve, especially when its 
motion is irregular. Take first the typical case represented by 
PI. I, where the centre-lines of the crank and connecting-rod 
and the eccentric and eccentric-rod coincide in the side elevation. 
Choose any piston-displacement and lay off AH, the displace- 
ment of the cross-head, equal to it; with the length of the con- 
necting-rod as a radius cut the circular path of the crank-pin 
at C, thus determining the crank-angle CO A. Make COF a 
right angle and lay off the angular advance FOE. With E, the 
centre of the eccentric, as a centre and with a radius equal to 
the length of eccentric-rod, cut the path of the end of the valve- 
spindle at h. Then ah is the displacement of the valve from 
its middle position, corresponding to the piston-displacement 
AH. In Fig. 1, PL II, take AA' to any convenient scale to repre- 
sent the stroke of the piston ; lay off the piston-displacement AH 



6 VALVE-GEARS FOR STEAM-ENGINES. 

of Fig. 4, PI. I, from A to the scale chosen and erect the ordinate 
Eth equal to the corresponding valve-displacement to any desired 
scale, not necessarily the same as the scale of abscissae. Very 
commonly the length of AA' is taken arbitrarily five or six inches 
while the ordinates are laid off full size. A sufficient number 
of points like h are constructed, with ordinates above the axis 
for displacements of the valve to the left of the middle position, 
and ordinates below the axis for displacements to the right. 
A smooth oval may be drawn through the points thus located, 
by aid of which the valve-displacement corresponding to any 
piston-position may be determined directly. Conversely, the 
piston-position can be determined for any valve-displacement; 
thus, if a valve-displacement Ao is taken, the corresponding piston- 
position, found by drawing a horizontal line, and an ordinate at 
the intersection with the oval, may be 0.88 of the forward stroke. 

The oval of Fig. 1, PI. II, is very irregular because both 
connecting-rod and eccentric-rod are short. If the length of the 
eccentric-rod is fifteen (or more) times the eccentricity, the valve- 
displacement may be found with sufficient approximation by 
making it equal to Oe in Fig. 1, PL I, found by dropping Ee 
perpendicular to the axis XX. In such case the oval will be less 
irregular than that of Fig. 1, PL II. If both the piston-motion 
and the valve-motion are harmonic, the oval becomes an ellipse 
like that drawn with a dotted line in Fig. 1. Though the figure is 
always an oval in practice, on account of the irregularity of motion 
due to the connecting-rod, it is customary to call it the valve- ellipse. 

To use the valve-ellipse (or oval) for studying the valve- 
motion it is customary to draw horizontal lines 00' and 0\Ox 
parallel to the axis AA' at distances equal to the steam-laps. 
In the figure these are equal. In like manner the lines ii and 
i x ii are drawn at distances equal to the exhaust -laps. It has 
already been pointed out that a valve-displacement equal to the 
steam-lap will bring the edge of the valve to the edge of the port 
and that the valve is in such position when it is (1) opening at 



PLAIN SLIDE-VALVE. 7 

admission or (2) closing at cut-off. An inspection of the figure 
shows that head-end admission occurs at 0.02 of the stroke before 
the dead-point, and that head-end cut-off occurs at 0.88 of the 
stroke, during the forward stroke. The crank-end admission 
comes just before the dead-point, and crank-end cut-off comes 
at 0.72 of the stroke, during the return stroke. Head-end com- 
pression occurs at 0.17 and head-end release at 0.98 of the stroke; 
and crank-end compression comes at 0.06 and release at 0.92 
of the stroke. The lead for the forward stroke is on, and for the 
return stroke o^n'. The inequality of the leads is due to the 
short eccentric-rod ; in practice such an inequality does not occur, 
first, because the eccentric-rod is longer, and, second, because the 
usual method of setting the valve makes the leads equal. 

The valve-ellipse may be advantageously used to investigate 
the action of a valve having an irregular motion, such as is given 
by some special valve-gears to be studied later, and it should 
be drawn during the design of the valves for every important 
engine. The motion of valves of an existing engine may be 
investigated by causing the engine to draw its own valve- ellipse. 
For this purpose, a reduced copy of the piston-motion, obtained 
by aid of a pantograph or otherwise, may be communicated to a 
slip of paper on which is pressed a pencil that derives its motion 
across the slip of paper from the valve-gear. The oval thus 
drawn will have the piston-displacements for abscissa? and the 
valve-displacements for ordinates, and should be identical with 
the valve-ellipse drawn to the same scale; any discrepancy must 
be due to mechanical defects in the valve-gear. 

Sinusoidal Diagram. — A diagram called by this name, be- 
cause the curves resemble sinusoids, was devised by Moll and 
Montety for use in designing valve-gears, taking account of the 
irregularities of both the piston and the valve. Starting at A, Fig. 2, 
Plate II, the crank-angles are laid off as abscissae toward A"\ and 
both the piston-displacement and the valve-displacement for a 
given crank-angle are laid off as ordinates, thus giving two curves, 



8 VALVE-GEARS FOR STEAM-ENGINES. 

AA'"A", representing the piston-motion, and nn'n, representing 
the valve-motion. The dotted lines are true sinusoids, and 
would represent the piston- and valve-motions if both were har- 
monic. The lines oo'o, 0\0\0\ are drawn to represent the steam- 
laps, and the lines ii'i, i\i\i\ to represent the exhaust-laps, 
which may or may not be equal. Inspection of the diagram 
shows that cut-off occurs at the crank-angle 133° and at a 
piston-displacement equal to ab. Conversely, if the cut-off is 
desired to take place at the piston-position ab, draw the line 
b'b" parallel to A A" and at a distance from it equal to the desired 
piston-displacement; from b, the intersection with the curve of 
piston-displacements, draw the ordinate ab; then ac is the lap 
which will give the desired cut-off. It is convenient to draw the 
curve of piston-displacements on a sheet of paper on a drawing- 
board, and to draw the curve of valve-displacements, which may 
be extended to give about one and a half revolutions, on a piece 
of tracing-paper or tracing-cloth. By superimposing the tracing 
of the valve-displacements on the drawing of the piston-displace- 
ments, and slipping it along as desired, the effect of using differ- 
ent values for the angular advance may be readily determined; 
at the same time the effect of different laps may be determined, 
or the lap for a special purpose may be found. 

This diagram cannot be conveniently substituted for the valve- 
ellipse, since it does not present to the eye the character of the 
valve-motion combined with the piston-motion; a valve-ellipse 
can readily be drawn from the sinusoidal diagram 

Zeuner's Diagram. — In the design of a plain slide-valve, and 
the greater part of all steam-engine valves, it is customary to pro- 
ceed as if the motion of the valve were harmonic; if any correc- 
tion is required it is left as an adjustment to be provided either 
in the completion of the design or in setting the valve. A num- 
ber of arbitrary circular diagrams have been devised for the 
purpose of designing slide- valves; though differing in appearance 
they are essentially similar in principle and any one can be used 



PLAIN SLIDE-VALVE. 9 

to solve all the problems that arise in practice. The most com- 
monly used circular diagram is one devised by Zeuner; it would 
be desirable that some one diagram should be accepted by en- 
gineers to avoid labor and misunderstanding. 

Zeuner's diagram is represented by Fig. 7, PL II, where XOX' 
and OY are a pair of rectangular axes, and the crank is given a 
left-handed rotation, as shown by the arrow; this arrangement 
corresponds to the trigonometrical convention and is often 
chosen whatever may be the actual construction of the engine. 
The angle YOP = d, equal to the angular advance, is laid off 
toward the crank; OP is made equal to the eccentricity, and 
on it is drawn the valve-circle ONP; then the valve-displacement 
for a given crank-angle 6 is equal to the chord ON, cut off by 
the valve-circle from the centre-line OR of the crank. 

A geometrical proof may be made by first locating the centre of 
the eccentric at p on the line Op which makes the angle 90° + $ 
with the position of the crank ; for harmonic motion the valve-dis- 
placement is On, found by dropping a perpendicular from p onto 
the axis XX r . Now draw the line PN, making the angle at N a 
right angle because it lies in a semicircle. The two right-angle 
triangles OP AT and Opn are equal because they have the sides OP 
and Op equal and the angles PON and pOn are both equal to 
180 — 90 — d — d. Consequently ON is equal to On equal to 
the valve-displacement. 

For comparison with certain future work, notably on link- 
motions, it is worth while to notice that if On is represented 
by e, and the eccentricity by r, we have 



as given by equation (6), page 123. 

Attention should be called to the facts that the diagram 
is entirely arbitrary, that it gives a correct result, and that it is 
found in practice to be very convenient; and that these con- 
siderations justify its use. 



io VALVE-GEARS FOR STEAM-ENGINES. 

The valve-circle of Fig. 7, PI. II, represents the motion of the 
valve to the left from middle position, and back again to middle 
position. It is clear that the chord cut from the centre-line of 
the crank will increase in length as OR approaches OP, and that 
the length of the chord will be zero when OR is at right angles 
to OP, for which crank-position the valve will be in mid-position. 
Fig. i, PL III, gives two valve-circles, one above the axis which. 
gives valve-displacements to the left, and one below the axis 
which gives displacements to the right. By the aid of this latter 
diagram the entire action of the valve may be represented in 
detail. 

Across the upper valve-circle is drawn an arc 00' , with a 
radius equal to the steam-lap that controls the flow of steam to 
the head end of the cylinder; this cuts the valve-circle at two 
points, through which are drawn the crank-positions OA h and 
OCu- At A h the valve-displacement is just equal to the steam- 
lap and the valve is at admission in the position represented by 
Fig. 4, PL II, moving to the left to open the valve, as is evident 
from a consideration of the arrangement of the mechanism of 
Fig. 1, PL I, and also from the fact that as the crank moves 
toward the left the length of the chord cut from the crank by the 
valve-circle increases. At the dead-point OX, the valve-dis- 
placement is equal to On = Oo + on, that is, to the lap plus on, 
the lead ; the valve is in the position shown by Fig. 3, PL II. As 
the crank moves forward the valve moves farther to the left and 
opens the port wider till the maximum displacement is attained, 
when the crank coincides with OP ; the valve is then in a position 
represented by Fig. 6, PL II, giving the maximum port-opening 
o'P, which in this case exceeds the width of the port. As the crank 
moves forward from the position just considered, the displace- 
ment decreases and the valve moves toward the right until at 
Ch the edge of the valve comes again to the edge of the port, but 
the valve now closes the port and interrupts the flow of steam to 
the cylinder; this action is known as cut-off. 



PLAIN SLIDE-VALVE. II 

Another arc, ii\ is drawn across the upper valve-circle, with 
a radius equal to the crank-end exhaust-lap, which controls the 
flow of exhaust from the crank end of the cylinder. A line 
OK c drawn through the intersection of this arc with the valve- 
circle shows the crank-position when the displacement of the 
valve is equal to the exhaust-lap, and the valve is in the position 
represented by Fig. 5, PL II, moving to the right to close the 
valve and interrupt the exhaust at compression. The valve 
now closes the ports at both ends of the cylinder so that 
steam cannot enter or leave, and that condition persists till 
the valve opens for release at the head-end at the crank-posi- 
tion Ru\ this crank-position is drawn through the intersection of 
the lower valve-circle with the head-end exhaust-lap arc drawn 
through i" . In this case the two steam-laps and the two exhaust- 
laps are equal; sometimes the laps are unequal, in which case 
the head-end steam-lap and the crank-end exhaust-lap, both drawn 
across the upper circle as in Fig. 1, PI. V, are usually the larger.. 
In any case the lap-arcs may be restricted to the circle to which 
they belong to avoid possibility of confusion. 

The events of the stroke thus far considered are admission 
just before the forward stroke begins, cut-off which commonly 
comes after half stroke, and crank-end compression and head-end 
release toward the end of the stroke. Having the crank-end 
steam-lap arc drawn through o' r the other events of the stroke 
are admission at A c , cut-off at C c , head-end compression at K h 
and crank-end release at R c ; the valve is displaced to the right 
at all these events; at admission the valve is moving toward 
the right, but at the other events the valve is returning toward 
the left. 

Though it is not customary to do so, the two arcs tt't", ss's' r 
may be added to find the crank-positions at which the edge of 
the valve is on the further edge of the port, and the port is 
wide open. The radius Of is made equal to the width of the 
port plus the steam-lap; when the crank-position passes 



12 VALVE-GEARS FOR STEAM-ENGINES 

through t or t" the displacement of the valve is equal to the lap 
plus the width of the port and the port is then wide open. In 
like manner the radius Os' is made equal to the width of the port 
plus the inside lap, and when the crank-position passes through 
5 or s" the port is wide open for exhaust. 

The diagram shows that the outside edge of the valve over- 
travels the edge of the port by the amount t'P. Some over- 
travel is desirable, as it gives in general a better action to the 
valve. The over-travel of the valve for exhaust is s'P, which 
is greater than t'P by the amount of the difference of the 
steam- and exhaust-laps.. The amount by which the port is open 
at any position of the valve is called the port-opening. The 
maximum port-opening for supply, which occurs when the crank 
coincides with OP, is equal to o'P, the difference between the 
eccentricity and the lap. The maximum port-opening for exhaust 
is equal to i'P. In this case the maximum port-openings are 
greater than the width of the port. A slide-valve moved by an 
eccentric always has the maximum port-opening for exhaust at 
least as great as the width of the port, and it is commonly 
greater; the maximum port-opening for supply is also commonly 
greater than the width of the port, but it is sometimes less. A 
slide-valve moved by a gear that gives a variable cut-off, as 
will be seen later, may have both maximum port-openings 
less than the width of the port for some settings of the gear. 

An inspection of the diagram Fig. i, PI. Ill, will show that 
a change of the steam -lap will affect both admission and cut- 
off ; thus, the cut-off is hastened and the admission is delayed 
by an increase of the steam-lap, and conversely the admission 
y comes earlier and the cut-off comes later if the steam-lap is 
^decreased. In a similar way, increasing the exhaust-lap delays 
the release and hastens the compression, while decreasing that 
lap produces a contrary effect. Since it is the relative propor- 
tions of lap and eccentricity which determine the cut-off, it is 
apparent that decreasing the eccentricity with a constant lap 



PLAIN SLIDE-VALVE. 13 

produces the same effect as increasing the lap with a constant 
eccentricity; i.e. it hastens the cut-off and delays the admis- 
sion. Finally, it will be seen that increasing the angular advance 
hastens all the events of the stroke; and that decreasing the angu- 
lar advance delays all the events of the stroke. 

Should the exhaust-lap of the valve be made nothing, so that: 
in mid-gear its acting edge coincides with the edge of the 
port, then both compression and release will occur when the 
crank is at right angles to POP' . Sometimes, in designing or 
remodelling a valve, it will be found advisable to give a clear- 
ance to the valve instead of an exhaust-lap, as represented by 
Fig. 2, PL IX, in which case the valve must be displaced to the 
right to bring the crank-end exhaust-edge of the valve to the edge 
of the port as is indicated by Fig. 3. Compression consequently 
comes at OK c drawn through the intersection of the lower valve- 
circle with the crank-end exhaust-clearance arc. Conversely, 
release, which is controlled by the head-end exhaust-edge of the 
valve, will occur when the valve is displaced to the left an amount 
equal to the head-end exhaust-clearance and will come before 
the crank-end compression. In order to emphasize the fact that 
the change from exhaust-lap to exhaust-clearance on the crank- 
end of the valve shifts the construction as shown in Fig. 1, PL. 
IX, to the lower valve-circle, the construction for head- end re- 
lease is omitted; it can be made by drawing the exhaust-clear- 
ance arc for the head-end of the valve across the upper circle, 
and will indicate that release comes between OC h and OK c . It 
is very important that the effect of giving the valve a clearance 
shall be clearly understood so that confusion cannot arise either 
in this place or in future work. 

Expansion and Compression. — From cut-off at OC h (Fig. 
1, PL III) to release at OR^, the head-end of the cylinder is shut 
off from both the supply and the exhaust. While the crank: 
moves forward from C^ to Rh, the piston moves a corresponding 
amount, and the steam in the cylinder expands and experiences 



i 4 VALVE-GEARS FOR STEAM-ENGINES. 

a loss of pressure in consequence; this action is called the ex- 
pansion. When the valve closes the exhaust at OK h the steam 
then caught in the cylinder is compressed ahead of the piston 
till a new supply of steam is admitted at OA h ; this action is called 
the compression. For the crank-end of the cylinder, in a like 
manner, steam is expanded from OC c to OR c , and is compressed 
from OK c to OA c . 

Lead and Lead-angle. — The lead, or the amount that the 
valve is open when the engine is on a dead-point, varies with 
the type and size of the engine, from a very small amount (or 
even nothing) up to half of an inch or more. Stationary engines 
running at slow speed may have from -fa to T V of an inch lead. 
The effect of compression is to fill the waste space at the end 
of the cylinder with steam; consequently engines having much 
compression need less lead. Locomotive-engines having the 
valves controlled by the ordinary form of Stevenson link-motion 
may have a small lead when running slowly and with a long cut- 
off, but when running at high speed with a short cut-off the 
lead is at least \ of an inch ; and locomotives that have a valve- 
gear which gives constant lead commonly have \ of an inch 
lead. 

In the solution of problems it is sometimes convenient to use 
the lead-angle, A h OX, Fig. i, PI. Ill, instead of the lead on. The 
lead-angle is likely to vary from zero to 8°; 2|° is a convenient 
angle for the solution of problems. 

Problems on the Slide-valve. — By assuming various elements 
of the valve-gear to be known a series of problems relating to 
the plain slide-valve may be stated and solved. A few of these 
problems which will be stated and solved are of real importance 
to the engine-designer. 

Problem I. Given the eccentricity, the lead-angle and the 
crank-angle at cut-off, to find the angular advance, the lap and 
.the lead. 

In Fig. i, PI. IV, draw, to any convenient scale, the arc 



PLAIN SLIDE-VALVE. 15 

XCX' to represent the path of the crank, referred to the axes 
XOX' and OY. Lay off the angle XOA equal to the lead- 
angle, and lay off XOC, the crank-angle at cut-off. Should the 
piston-position at cut-off be given instead of the crank-angle, 
find the crank-position OR c corresponding by the method used 
for the valve-ellipse, p. 5. With equal leads the laps and crank- 
angle at cut-off will be the same for each stroke, and the mean 
piston-position will be nearly equal to the piston-position at cut- 
off with harmonic motion. In such case the crank-angle at cut- 
off may be found by laying off Xr equal to the given piston-dis- 
placement at cut-off and drawing the vertical line rC. 

Bisect the angle AOC and draw the line OP; on it draw 
the valve-circle O0P0'" , and through the intersections of this 
valve-circle by the lines OA and OC draw the lap-arc 00'". The 
lead is o'a. 

In Fig. 1 the eccentricity is i| of an inch, the cut-off is at 
f of the stroke, and the lead-angle is 2J . The lap is ff of an 
inch, and the lead is -fa of an inch; the angular advance is £ = 31^°. 

Problem II. Given the eccentricity, the lead, and the crank- 
angle at cut-off, to find the angular advance and the lap. 

In Fig. 4, PI. IX, lay off the angle XOC equal to the crank- 
angle at cut-off, and draw the arc CPb with a radius equal to 
the eccentricity. From b draw an arc with a radius equal to 
the lead, and from C draw CA tangent to that arc. Draw a line 
OA through the point A, and bisect the angle CO A* by the 
line OP perpendicular to CA. Draw the lap-arc mng, which 
will touch the line CA at the point n; it may be noted that 
the triangle A On is equal to the right triangle OPg formed by 
drawing the line Pg, because they have the sides OP and OA 
equal and have the angle POA in common, and consequently 
On is equal to Og. 

The construction gives of for the lead which must be equal 
to the assumed lead, i.e. equal to be. To prove this equality 
draw the line Pj and drop the perpendicular bk from b onto OP, 
thus forming the two equal right triangles OPf and Obk, which 



1 6 VALVE-GEARS FOR STEAM-ENGINES. 

have the sides OP and Ob equal and the common angle POb; 
the two sides Of and Ok are equal, and taking away the equals 
Oo and On there will remain 

of=nk = be, 

as required for the construction. 

In the problem discussed the eccentricity is assumed to be 
known and direct solutions are readily found. Very often the 
designer has sufficient information to proceed in this way, or he 
may assume a series of values for the eccentricity and in a few 
minutes have a series of results from which he can select the 
eccentricity that will give satisfactory proportions for the valve. 

Now the real object of the gear is to open the steam-port and 
the designer must decide whether the port-opening is sufficient 
and whether the valve opens and closes rapidly enough. Refer- 
ring again to Fig. i, PL III, it appears that the valve begins to 
open at OA u and that the port is wide open when the crank 
reaches a position that can be located by drawing a line through 
O and t, because in that figure Oo' is equal to the lap and o't' is 
equal to the width of the port. During this action the valve 
moves rapidly, and in like manner the valve moves rapidly while 
the valve is closing. After the port is wide open the valve 
moves more and more slowly till it stops when the crank coin- 
cides with OP, when the port-opening exceeds the width of the 
port by the amount t'P. Such a favorable action for the sup- 
ply of steam is possible only for comparatively small and slow 
engines. Very often the maximum port-opening for large engines 
is from two-thirds to three-fourths of the width of the port. 
The maximum exhaust port-opening, which is greater than the 
steam port-opening, is always equal to the width of the port and 
usually larger. 

The method of determining the area and thence the width of 
the port will be given on page 36. Having the width of the port, 
the designer may determine the desirable or the possible maxi- 



PLAIN SLIDE-VALVE. 1 7 

mum steam-port opening. He may then determine the proper 
eccentricity by trial as just explained, or he may make a deter- 
mination by the following method. 

Problem III. Given the maximum port-opening, the crank- 
angle at cut-ojj, and the lead-angle, to find the eccentricity, the lap, 
and the angular advance. 

Assume an eccentricity, preferably a little larger than that 
required, and solve the problem by the method of Problem I, by 
drawing the crank-positions at OA and OC for admission and 
cut-off, and bicecting the angle AOC and drawing the valve-circle 
OP\. Draw the lap-arc qq" , thus determining the maximum 
port-opening q"P\. From this trial port-opening and eccen- 
tricity, and the desired port-opening, determine the proper eccen- 
tricity by the following proportion : 

Assumed Required Assumed Required 
port-opening : port-opening : : eccentricity : eccentricity ; 

which is evident from the similarity of the figures. 

In the case represented by Fig. 2, PI. IV, the desired port- 
opening is I of an inch; an eccentricity of if of an inch gave a 
port-opening of f f of an inch, so that the proportion 

29 .1. . T 3 7 

gave e=i ^g of an inch. 

With this eccentricity the second valve-circle OP is drawn, from 
which all the elements of the valve may be taken. 

In general, it is preferable to solve the proportion numerically, 
but if desired a graphical solution may be made as follows: Lay 
off the line Oc x = q"P 1 , in a convenient position, and join e\C\\ 
make Oc equal to the given maximum port-opening, and draw 
ce parallel to c\e x ; then e is the centre of the required valve- 
circle and OP is the required eccentricity. 

Modifications. — In general it is not of great importance that 
the cut-off shall occur exactly at the chosen crank-angle or piston- 
position, and it is seldom necessary to know the angular advance 



io VALVE-GEARS FOR STEAM-ENGINES. 

except in drawing the valve-diagram. It is, however, very con- 
venient if not necessary that the lead and lap shall be deter- 
mined quantities stated in fractions of an inch that are commonly 
used in the machine-shop. By judicious modifications the de- 
signer may secure this for the valve without seriously affecting 
the point of cut-off. In Fig. 3, PI. IV, the lap, Oo, is made f of 
an inch, and the lead is -^ of an inch. At a the vertical aP is 
drawn, and from O, with a radius equal to ij of an inch, the 
vertical is intersected in P; thus giving the diameter OP on which 
the valve-circle OaPo" is drawn. The cut-off comes at the crank- 
position OC, corresponding to the piston-displacement Xr instead 
of Xt=l stroke, as required. 

The process of laying out a slide-valve will be considered in 
connection with the valve for equal cut-off. 

Equalization of Cut-off at the Expense of the Lead. — Let it 
be assumed that the cut-off shall occur at a given piston-position 
for each stroke, taking account of the irregularity due to the con- 
necting-rod. Draw the line xX', Fig. 1, PL V, on which choose 
O for the centre of the crank and for the origin of coordinates, 
and draw the vertical axis YOY f . Draw the circle XYX'Y', to 
any convenient scale, to represent the crank-circle. With a radius 
equal to the length of the connecting-rod, on the same scale, and 
with X and X' as centres, cut the centre-line X'x at x and x f ; 
this will give the stroke of the cross-head, equal to the stroke of 
the piston. Lay off the point on the stroke at which cut-off is 
to occur on both strokes, and with these points as centres and 
the length of the connecting-rod as a radius intersect the crank- 
circle at Cft and C c . In the figure the connecting-rod is taken 
to be five times the crank, and cut-off is assumed to occur at f 
of the stroke. It is at once apparent that the crank-angles XOCh 
and X'OC c are not equal, and OC h and OC c are not one straight 
line. Choose a small head-end lead-angle XOA h ; in the figure 
it is 1° Bisect the angle A h OCh, and draw the line POP, on 
which draw the two valve-circles as shown. The eccentricity 






PLAIN SLIDE-VALVE. 19 

iriay be determined by a preliminary solution, assuming harmonic 
motion, as in Problem III, or the same solution may be made 
directly on the figure; if the latter method is used, confusion is 
liable to occur from the number of circles drawn, especially if 
the eccentricity is modified to get some convenient dimension; 
consequently it is better to make such a construction separately 
and transfer the results to the main diagram. Draw the lap-arc 
00 for the upper valve-circle, through the intersections of that 
circle by OA h and OCh] and draw the lap-arc o'o' for the lower 
valve-circle, through the intersection OC c with that circle. The 
admission at OA c occurs at the intersection of the lower valve- 
circle and the lap-arc o'o'; as a result the crank-end lead is large, 
if not excessive. 

It is customary, in designing a valve for equal cut-off, to 
equalize the compression also. In Fig. 1 the compression is 
assumed to occur at f of the stroke, or at the crank-positions OK h 
and OK c . The exhaust-laps are ii and i'i', so that the release 
•occurs at Rh and R c . The point of intersection i of the line OKh 
with the valve-circle may be determined by dropping a perpen- 
dicular Pi from P on OK h . The valve-diagram in Fig. 1 gives 
the following dimensions: 

Eccentricity 1 § inch 

Steam-lap, head- end f J " 

" crank-end ff " 

Exhaust-lap, crank- end A " 

" head-end & " 

Lead, head- end & " 

' ' crank-end if " 

On account of the excessive crank-end lead which is likely 
to result when this method is applied to an engine which has a 
short connecting-rod, it is customary to make a compromise; 
the head-end lead is made as small as practice shows to be allow- 



zo VALVE-GEARS FOR STEAM-ENGINES. 

able and the crank- end lead is made as large as allowable; the 
head-end cut-off will then be longer than the crank-end cut-off, 
but the inequality will be less than if the leads were equal. 

To Lay out a Slide-valve. — The valve for which dimen- 
sions were found in Fig. i, PI. V, is shown in section by Fig. 2. 
To lay out the valve, begin at the crank end and make a& = || 
of an inch, equal to the crank-end steam-lap; make bc = rs of 
an inch, equal to the width of the port. 

The greatest displacement of the valve, equal to the eccen- 
tricity 1 J of an inch, will carry the point a to a f , and when the 
valve is in that position it must not overrun the edge of the 
bridge, but rather there must be width enough remaining to 
prevent leakage. The least width of bridge in the figure is ff 
of an inch, and the width of J inch is chosen to insure a joint. 

The crank-end exhaust-lap, A of an inch, is laid off at cd. 
The greatest displacement of the valve will carry the point d 
to d', and at that position of the valve the remnant of the exhaust- 
space should be at least as wide as the port, i.e. A of an inch 
as shown. The exhaust-space is commonly made wider than 
this construction gives; it should not be unduly increased, since 
it will then make the valve large and the friction excessive. 

The valve is completed by making the width of the bridge 
I of an inch and of the port, A of an inch, as shown. If the 
eccentricity, 1 \ of an inch, be laid off toward the left, from the 
right-hand edges of the valve, it will appear that the right-hand 
bridge is wider than necessary, and that the remnant of the 
exhaust-space, when the valve has its maximum displacement 
to the left, is greater than the width of the steam-port. No 
inconvenience will occur from such an excess of bridge or ex- 
haust-space; but had the construction been begun at the right- 
hand, then both the bridge and the exhaust-space would be 
too narrow, which explains why the drawing is begun at the crank- 
end. For constructive reasons, the bridge for any slide-valve 
may be made wider than required to prevent leakage. 



PLAIN SLIDE-VALVE. 21 

Fig. 3, PL V, gives the section (half-size) of a valve with 
equal laps, which will give the same average cut-off as the valve 
shown by Fig. 2; the cut-off at the head-end will be longer, and 
that at the crank-end will be shorter. The steam-lap for Fig. 3 
is very nearly the mean of the unequal steam-laps of Fig. 2; 
and the exhaust-lap is very nearly the mean of the exhaust-laps 
of the same figure. Such a valve may be laid off, beginning at 
either end. 

The height of the exhaust-cavity of the valve should never 
be less than the width of the steam-port; it may conveniently 
be made equal to the width of the port plus half the width of 
the bridge. 

The method just given for laying out the slide-valve has 
the apparent inconvenience, that the centre of the exhaust-space 
cannot be directly located on the assembly drawing of the engine. 
This difficulty is, however, only apparent, for the section of the 
valve is commonly drawn separately and at full size, and then 
•can be transferred to the assembly drawing, which may be to 
any convenient scale. The results obtained by laying out the 
work on the drawing-board should always be checked by a 
numerical calculation; and if desired such a numerical calcula- 
tion may be made first, but it should be checked by the subsequent 
laying out of the valve. Thus the width of the bridge should 
be greater than 

ii— U— &=ff, or nearly f of an inch; 

and the exhaust-space should have a width of 

A + il+A-l = ii- of an inch. 

Rocker and Bell-crank Lever. — In the work thus far it has 
been assumed that the centre-lines of the crank and connecting- 



22 VALVE-GEARS FOR STEAM-ENGINES. 

rod with the cross-head and piston, and of the eccentric and 
eccentric-rod with valve-spindle and valve, coincide in the eleva- 
tion, as shown by Fig. i, PI. I. This assumption is convenient 
in giving the first description of the valve-gear and in discussing 
the action and the theory of the valve-motion; and the design 
of the valve is commonly carried on as though such a coincidence 
existed, the deviation from such a coincidence being considered 
only in the mechanical problem of laying out the mechanism of 
the engine. 

If the centre-line of the valve-spindle passes through the 
centre of the shaft, and the eccentric-rod is connected directly 
to the valve-spindle, then the motion of both crank and connect- 
ing-rod, and eccentric and eccentric-rod, referred to their own 
proper axes, will be the same as already found, even though their 
centre-lines do not coincide. Such a lack of coincidence will 
make the angle between the eccentric and the crank more (or less) 
than 90 plus the angular advance, by the amount of the angle 
between the two centre-lines. This difference needs considera- 
tion only in the process of setting the valve; and if the angle 
between the centre-lines is small, it will require little or no atten- 
tion at that time. Since such an arrangement involves a lack 
of parallelism between the paths of the valve and of the piston, 
the work of boring the cylinder and facing off the valve-seat is 
more troublesome, and other machine-work is more difficult, 
unless special processes are provided; consequently this arrange- 
ment is seldom adopted. 

Very commonly the paths of the piston and the valve are 
parallel but do not coincide in the elevation; thus, the axis of 
the crank and connecting-rod with the cross-head and cylinder 
may be XX' in Figs. 2, 3, and 4, PI. Ill, while the centre- 
line of the valve-spindle may be xx f in the same figures. In 
such cases a rocker or a bell-crank lever should be used to trans- 
mit motion from the eccentric to the valve. 

The following method may be used in laying out a bell- 



PLAIN SLIDE-VALVE. 23 

crank lever. Let A be the position of the end of the valve- 
spindle when the valve is in mid -position; lay off A a and A a' 
equal to the steam-laps of the valve, and with a radius equal to 
the length of the arm of the bell-crank lever draw arcs inter- 
secting at C; this gives the axis about which the bell-crank 
lever vibrates. This construction prevents the bell-crank lever 
from introducing any irregularity into the action of the valve 
at admission and cut-off, because the valve-spindle at those 
events has its proper displacement; irregularities at other times 
are of less consequence. In laying out such a gear for a loco- 
motive with a rigid valve-spindle that extends directly from the 
end of the bell-crank lever or rocker to the valve-yoke, it is 
important to have the bending or lateral motion of the valve- 
spindle as small as possible; in such case the point C may be so 
chosen that the lateral motion of the end of the valve-spindle shall 
be half above and half below the line xxf. 

With a radius equal to BC, the other arm of the bell-crank 
lever, draw . an arc as shown, and draw a tangent to this arc 
from O. Draw perpendiculars OE and CB from O and C to 
this tangent; then EB is the length of the eccentric-rod; this 
construction tends to minimize irregularity due to the eccentric- 
rod and the rocker. If desired, the relation of the crank and 
eccentric may be found by laying off the angle XOR = d, the 
angular advance, since the crank is at that angle before the dead- 
point when the valve is in mid-position ; the angle EOR will not 
be equal to 90 + d, but this is a matter that affects the valve-setting 
only, and even in that process the exact knowledge of the angle 
between the crank and eccentric is not of importance.' 

If it is considered of importance that the eccentric-rod shall 
be some definite length, then the centre C, on which the bell- 
crank lever vibrates, may be shifted so as to give that length. 
If C is to be shifted a short distance, then a line parallel to XX' 
may be drawn through B, and with a radius equal to the desired 
length of the eccentric-rod an arc may be drawn frap^inter- 



. 



24 VALVE-GEARS FOR STEAM-ENGINES. 

secting that parallel line at a point B'; the whole bell-crank 
lever is to be shifted bodily to the extent BB' , and the length of 
the valve-spindle must be changed the same amount. 

In the figure the arm CB is made f of CA ; consequently 
the motion of the valve will be that which would be given by 
an eccentric equal to f of OE if the connection were direct. In 
designing and laying out the valve it is treated as though it were 
moved by such an eccentric. The ratio of the arms may be 
made anything desired; they have commonly the same length. 

In laying out a rocker, the process is the same as that just 
described for the bell-crank lever, except that the arm CB, Fig. 
3, is laid off on the side opposite A, and the eccentric follows 
the crank. 

Fig. 4 shows an equal-armed straight rocker with the centre 
of vibration C midway between the lines XX' and xod\ it may 
be made a little longer if desired so as to give a construction 
equivalent to that shown by aAa', Figs. 2 and 3. 

Angular Advance. — On page 4, angular advance is defined 
as the amount by which the angle between the crank and eccentric 
exceeds 90 , and that definition is correct and sufficient for the 
typical arrangement of Fig. 1, PI. I; and as slide-valves are 
usually designed as though that arrangement were to be used, 
the definition stated is the one commonly given and accepted 
by engineers. As a matter of fact it is only in the process of 
setting the valve that a deviation from this definition is recognized, 
and the one condition that usually brings the deviation into promi- 
nence is the use of a rocker, which requires that the eccentric 
shall follow the crank by an angle equal to 90 minus the angular 
advance, as indicated on Fig. 4, PI. III. Engine-setters are 
familiar with this condition and allow for it without special 
directions. A convenient mnemonic is to consider that the rocker 
reverses the motion of the valve and that to compensate, the 
eccentric must be reversed, i.e., shifted 180 . Sometimes, when 
a bell-crank lever or a rocker is used, as in Fig. 2 or Fig. 3, 



PLAIN SLIDE-VALVE. 25 

PL III, the eccentric is not exactly 90 plus (or minus) the 
angular advance from the crank; or if the centre-line of the 
valve-gear is shifted a small angle from that of the crank and 
connecting-rod, as explained on page 22, the same condition 
arises. The deviation . from the typical condition is usually 
small in such cases, and is not likely to be observed by the engine- 
setter; the engine-designer is liable to ignore the deviation if he 
gives it any thought. 

If an exact definition is desired it may be derived from Figs. 
2 and 3, PI. Ill, and stated as follows : the angular advance is the 
angle the crank makes with its line of centre when the valve is 
in mid-position. 

Equalization of Cut-off with Rocker. — In the directions 
for laying out a rocker or a bell-crank lever care is taken to avoid 
disturbing the valve-motion and for that purpose symmetrical 
constructions are used. Needless deviations from the methods 
given are likely to introduce undesirable irregularities into the 
valve-motion. On the other hand a judicious deviation from the 
. symmetrical constructions may introduce a desirable irregularity 
into the valve-motion which can be used to off -set the irregularity 
of the piston-motion which is due to the connecting-rod. 

The typical arrangement of the valve-gear represented by 
Fig. 1, PI. I, with a long eccentric-rod, will give nearly a harmonic 
motion to the valve. If the valve has equal laps the port-openings 
will be equal but the piston-positions at cut-off will be very unequal. 
An attempt to equalize the cut-off at the expense of the lead (and 
also of the port-openings) has already been shown to be unsatisfac- 
tory. To Professor Sweet is due the idea, that by the use of a 
bent-rocker an irregularity may be purposely introduced into 
the valve-motion which may be made to equalize the cut-off 
without interfering with the equality of the lead; in this case 
the inequality of the port-openings may be excessive. 

On Plate VI an example is given of such a use of a bent rocker 
to equalize the cut-off of a valve which is designed to give cut- 



26 VALVE-GEARS FOR STEAM-ENGINES. 

off at fths stroke. In the first place the valve-circle is drawn as 
for harmonic motion for both piston and valve. That is, the 
diameter of the crank-circle XX' is divided into quarters and 
a vertical line through the f ths mark iVis drawn intersecting the 
crank-circle at C, and the crank-position OC is drawn; the dotted 
circle which represents the path of the eccentric happens to 
pass through N because the eccentricity was taken equal to one- 
half the crank. The crank-positions at admission OA h and 
OA c are also drawn and these remain fixed during the follow- 
ing constructions. Bisecting the angle A h OC by the line OP 
determines the angular advance YOP, and on OP the valve- 
circle is drawn with the proper diameter, together with the lap-arc 
oo' which determines the lap for both ends of the valve for equal 
lead. The valve design is to be completed in the usual way and 
the valve and seat are to be laid out. The remainder of the 
discussion has to do with the design of the rocker and its effect 
on the motion of the valve. 

The usual harmonic action of the valve with a symmetrical 
rocker will give cut-off at the head end when the piston is some- 
what beyond fths stroke, and the crank-end cut-off will come earlier 
than fths stroke; the mean piston-position at cut-off will be very 
nearly at fths stroke. The object of the use of the bent rocker 
is to bring the valve to the position of cut-off when the piston 
is at fths stroke for both strokes of the engine. With the length 
of the connecting-rod as a radius and with X and X' as centres, 
determine the stroke xx' of the cross-head and divide it into 
quarters; with the fths points as centres and the connecting-rod 
as a radius, determine the crank-positions C h and G c correspond- 
ing to the desired piston-positions at cut-off. Since a rocker 
is to be used the normal position of the eccentric is co° minus 
the angular advance after the crank; the angle to use for this pur- 
pose is XOP. Laying off this angle to the right from OCh gives 
Or c for the corresponding position of the eccentric for head-end 
cut-off at fths stroke; in like manner Or a corresponds to I 



PLAIN SLIDE-VALVE. 27 

OA h , Or c f corresponds to OC c and 0r a ' corresponds to OA c . 
With r c ' and rd as centres and with the length of the eccentric- 
rod as a radius, draw arcs intersecting at e; then if a rocker be 
constructed in such a way that the end of the eccentric-rod is 
guided to e when the eccentric is at r c ' and rd (that is, when 
the crank is at C c and A c ) and if the valve be so set that its 
displacement shall then be equal to the lap, the cut-off will 
come at fths stroke of the piston and the engine will also have 
the desired lead. In like manner, with r c and r a as centres, 
strike arcs intersecting at e x \ this last is the point to which 
the end of the eccentric-rod must be guided in order that cut-off 
may come at fths stroke for the head-end. With a con- 
venient length for one arm of the rocker as a radius, draw arcs 
from e and e x intersecting at 7\; this will be a proper centre 
for the rocker, and from it the path of the end of the eccentric - 
rod may be drawn through e and e\. The other arm of the 
rocker will be turned downward and its length must be such 
that the valve-displacements corresponding to the positions e and 
ei shall be equal to the steam-lap. Draw the chord ee x ; half 
of this chord will be found to be greater than the steam-lap Oo, 
consequently the other arm of the rocker must be proportion- 
ately reduced. A convenient construction is to lay off qs from 
the middle of the chord equal to the lap and through s draw a 
line parallel to eT\, cutting the line T x q at the point t; then 
st is the proper length for the other rocker arm. 

Thus far no attention has been paid to the position of the 
valve-spindle,, and it is altogether likely that a position of the 
rocker corresponding to the trial centre T\ will be practically 
inconvenient, and that the whole gear must be shifted to 
accommodate the location of the valve. Suppose that run' is the 
desired position of the valve-spindle; draw a line //' parallel to 
this position and at a distance equal to tq, and from O draw an 
arc through T x cutting IV at T\ this will be the proper posi- 
tion for the centre of the rocker. The mechanism for the guid- 



28 VALVE-GEARS FOR STEAM-ENGINES. 

ance of the eccentric -rod is to be swung through the same angle 
TiOT, so that the path of the end of the eccentric-rod will be 
found at cc Ci, of which the middle point may be found by draw- 
ing an arc from the centre O through the middle point e of the 
original construction and laying of an angle equal to T\OT. 
The eccentric centre must move with the rest of the gear so that 
its position corresponding to C\ will be r a ", with the angle r a 'Or a " 
equal to T\OT. The construction is completed by drawing 
Tao perpendicular to nn' and equal in length to ts, for the middle 
position of the lower arm of the rocker. The end of the rocker 
and the head of the valve-rod which communicates motion to the 
valve-spindle will move on the arc b r b, drawn with T as a centre; 
a and a' are the positions when the valve is at admission or cut- 
off. The extreme positions are b and b f , found by trial, which 
indicate that the port -openings are unequal. It may be desir- 
able to construct a valve-ellipse, taking account of all irregu- 
larities of the entire mechanism of piston and valve-gear, from 
which it may be decided whether or not the design is sufficient. 
Should the port -opening at one end appear to be really insufficient, 
it will be necessary to take a larger eccentricity and repeat the 
construction. 

Piston-valve. — If the section of a plain slide-valve and its 
seat, as shown by Fig. 3, PL I, be supposed to revolve about 
an axis xotf, there will be generated a piston-valve with its cy- 
lindrical seat. Such a valve is represented by Fig. 1, PL VII, 
which gives a section of the high-pressure cylinder and valve 
of the U. S. battle-ship Massachusetts. It will be seen that the 
outside shell of the cylinder, the lower cylinder-head, and the 
valve-chest form' one casting, with feet attached for bolting to 
the engine-frame. A cylinder-liner is forced into and secured 
to the outer shell, with a space between to serve as a steam- 
jacket. The piston is of conical form, and the heads are shaped 
to correspond. Leakage by the piston is prevented by two 
packing-rings held in place by a junk-ring. 



PLAIN SLIDE-VALVE. 29 

The piston-valve is in the shape of two pistons connected 
by a pipe or sleeve through which the valve-spindle passes. 
The valve-spindle is prolonged beyond the valve and attached 
to a small balancing-piston which relieves the valve-gear of the 
weight of the valve and attached parts; the upper end of the 
balancing-cylinder is connected with the exhaust. The valve- 
seat is formed by two short hollow cylinders, forced into the 
shell of the valve-chest. The space surrounding each half of 
the valve-seat is connected with and forms part of the port 
leading to the cylinder. The ports are cut through the cylin- 
drical valve-seat as shown. 

Steam is supplied to the middle of the steam-chest and is 
exhausted from the ends through pipes shown by dotted circles. 
This arrangement secures the advantages that the supply and the 
exhaust-steam are kept well separated so that heat cannot easily 
pass from one to the other, and the valve-rod stuffing-box is 
exposed to the exhaust -steam only; such an arrangement is 
not advisable for a cylinder in which there may be a vacuum, 
since the leakage of air inward, past the stuffing-box, is more 
troublesome than the escape of steam. 

The valve is drawn in mid-position to show the relation of 
the laps and other properties of the valve, and it is consequently 
not in proper relation to the piston, but no confusion need come 
from this disposition. The laps controlling the admission and 
cut-off are by this arrangement placed inside, while the laps 
controlling the release and compression are outside. It will be: 
noticed that the top- end steam-lap is the larger, while the top- 
end exhaust-lap is the smaller, and is here a negative lap or 
clearance. This arrangement is adopted to hasten the cut-off 
and compression on the down-stroke and delay them on the up- 
stroke, but is not carried far enough to produce complete equali- 
zation. 

Leakage past the valve is prevented by packing-rings, like 
those of the piston, which form the acting-edges of the valve. 



3° VALVE-GEARS FOR STEAM-ENGINES. 

To prevent the valve-rings from springing into the ports, bridges 
are left as shown at A. 

Double-ported Valve. — It is frequently difficult or impossible 
to get sufficient width of port for engines having a large cylinder 
diameter and short stroke, if the common plain slide-valve is to 
be used. Fig. 2, PI. VII, shows a device, known as a double- 
ported valve, used in marine engineering to overcome this diffi- 
culty. Each passage leading to the cylinder has two ports, and 
two slide-valves, joined together in one casting, to control the 
flow of steam through those ports. The inner valve resembles the 
common slide-valve, except that there is a communication through 
the top between its exhaust-space e and the exhaust-space e of 
the outer valve. The outer valve is elongated enough to leave a 
steam-space (a and a') to supply the inner valve ; a bridge between 
e and a separates the exhaust of the outer valve from the steam- 
space of the inner valve, and is continued to the opening through 
the top of the inner valve. Fig. 3 gives, at the left hand, a trans- 
verse section through the exhaust-space e, and at the right, through 
the steam-space a. The space a is drawn down toward the mid- 
dle of the valve as shown, so that the valve may be made compact 
while providing sufficient area for the flow of steam. 

Allen or Trick Valve. — Fig. 4, PI. VII, shows a valve which 
is so made that a double admission of steam takes place at and 
near cut-off and admission. It is used with the link-motion and 
other gears which give a variable cut-off with the slide-valve, and 
is intended to remedy the defects due to the slow motion imparted 
to the valve at those points when the cut-off occurs early in the 
stroke. 

Through the body of the valve there is a passage ss f , and the 
valve-seat is cut away so that the distance from the outer edge of 
the passage to the edge of the valve-seat is equal to the steam- 
lap of the valve. If the valve is displaced toward the right by 
the amount of the steam-lap, the edge c of the valve is brought 
to the edge of the port a, and at the same time the edge of the 



PLAIN SLIDE-VALVE. 3 1 

passage s' is brought to the edge d of the valve-seat. Conse- 
quently there is a double admission of steam to the port a, one in 
the usual way past the edge c, and the other under the right-hand 
end of the valve, past the edge d of the valve-seat, and through 
the passage s f s. As the valve opens wider, the passage ss' is 
liable to be shut off by traversing past the farther edge of the 
port a, but when that happens the supply past the edge c is 
abundant. Near cut-off the passage ss' is open at 5 and gives 
a double supply of steam till cut-off occurs by the simultaneous 
coincidence of c with the edge of the port a, and of d with the 
edge of the passage s'. This principle has been applied to give 
double admission to. piston-valves and other forms of valves, 
which appear to be different from Fig. 4, but which are essentially 
similar to it in this particular feature. 

Balanced Valves. — When the difference of pressure between 
the steam- and exhaust-pipes is large, the force exerted to hold a 
plain slide-valve against its seat is very large, and the friction of 
the valve on its seat is excessive. This consumes a needless part 
of the work developed by the engine, throws a severe duty on 
the valve- gear, and makes it difficult to maintain the acting- 
surfaces of the valve and its seat in good condition. Various 
methods of relieving valves from part or all of the steam-pressure 
on them have been devised, resulting in what are called balanced 
valves. 

The piston- valve (shown by Fig. 1, PI. VII) is not pressed 
against its seat by the steam, and is consequently perfectly bal- 
anced. It is very commonly used for the high-pressure and in- 
termediate cylinders of triple-expansion marine-engines, and on 
high-speed engines under the control of a shaft-governor. When 
well made, and provided with packing-rings, there is no more 
reason for leakage than exists with the piston of the engine. 
Small piston-valves are commonly made without packing-rings, 
and then depend on the fit in the valve-seat to prevent leakage. 
It is claimed that they do not leak when new, that the wear is 



32 VALVE-GEARS FOR STEAM-ENGINES. 

insignificant, and that both valve and seat may readily be renewed 
when necessary. It is, however, probable that such piston-valves 
do frequently leak in common service. 

The double-ported valve (Figs. 2 and 3, PI. VII) and the 
Allen valve (Fig. 4, PL VII) have part of the pressure on the 
back relieved, and are known as balanced valves. The double- 
ported valve has a shallow cylindrical recess turned in its back. 
In this is a short cylinder or ring that is pressed by springs against 
a finished surface on the valve-chest cover. A bronze ring fas- 
tened to the valve and bearing against the vertical ring or cylinder 
is intended to prevent leakage. Communication is opened be- 
tween the enclosed space and the exhaust, so that the leakage may 
not accumulate in this space and destroy the balancing of the 
valve. The unbalanced pressure of the steam on the unenclosed 
part of the valve gives enough pressure against the seat to prevent 
leakage. The Allen valve is commonly wider (measured at right 
angles to the axis of the cylinder) than it is long, and conse- 
quently a rectangular balancing-frame is used to exclude pressure 
from ■ part of the top of the valve. Leakage into the enclosed 
space is allowed to flow directly into the exhaust-cavity through 
a small round passage, shown by dotted lines. 

All such devices are somewhat costly to make and troublesome 
to maintain in good condition, and if allowed to get out of condi- 
tion are liable to a large loss from leakage directly into the exhaust. 

Valve-setting. — A slide-valve is commonly set to give equal 
lead, or else equal cut-off. Sometimes the leads are made un- 
equal, so as to partially equalize the cut-off; in this case the 
method of setting is like that used for equal lead, except that the 
lead at each end is made the amount determined on. If the 
cut-off is equalized by aid of a rocker or bell-crank lever, as 
shown on Plate VI, the valve is set to give equal lead. 

As a preliminary to the setting of the valve, a method will be 
given for putting the engine-crank on- the dead-centre. 

To put an engine on the dead-centre. — In Fig. 1, PL VIII, let 



PLAIN SLIDE-VALVE. 33 

the circle CoCCqC be the path of the crank-pin, and let AqAq' 
be the stroke of the cross-head; while abed represents the edge 
of the fly-wheel or the face of the crank-disk, if the crank is so 
made. Set the engine with the cross-head near the middle of 
the stroke, and make reference-marks at A, or take measurements 
so that it may be set again in the same position. Make a ref- 
erence-mark on the circle abed, and on some fixed object as, at a 
and o. Turn the engine around till the cross-head again comes 
to A ; the crank will then be at C, and the mark made at a will 
be found at c. Make another mark at a, and bisect the arcs 
dbc and adc at b and d. It is apparent that the angular distance 
of b from a is equal to the angular distance of C from Co ; con- 
sequently the crank will be at the dead-point Co', if the mark 
at & is brought opposite o. Also the crank will be at the dead- 
point Co when d is brought opposite o. 

In this process, and during all the operations of valve-set- 
ting, the engine and the valve-gear should always be moved in 
the direction in which the engine is intended to run, so that the 
lost motion or back-lash may be taken up in the right way. 
Should the engine or the gear be moved too far at any time, it 
should then be turned back beyond the desired point, and again 
brought up to that point with a motion in the right direction. 
Should the elasticity of the engine-belt interfere with the con- 
venient and accurate setting of the engine, it may often be pos- 
sible to place a stick of timber under a fly-wheel arm, block up 
one end and place a jack-screw under the other, and so force 
the engine to the desired setting and hold it at will; or some 
equivalent device may be used. 

To set a valve with equal lead. — First method. — Set the engine 
on a dead-point and give the eccentric the proper angular advance, 
as near as may be; making it too much rather than too little. 
Adjust the length of the eccentric-rod or of the valve-spindle 
to give the valve the proper lead. Move the engine forward 
to the other dead-point, and measure the lead; if it is not right, 



34 VALVE-GEARS FOR STEAM-ENGINES. 

then correct half the error by changing the length of the valve- 
spindle, and the other half by moving the eccentric. Repeat till 
the result is satisfactory. 

If a valve-gear has a rocker, then the length of the valve- 
spindle should be such that the rocker may swing as designed; 
usually to an equal angle on each side of a perpendicular through 
its axis, to the centre-line of the eccentric-rod motion. In such 
case the eccentric-rod only should be changed in setting the 
valve ; a small change of the valve-spindle may be allowed. 

Second method. — A valve that has harmonic motion will 
give the same maximum port-opening for each stroke when set 
with equal lead. Such a valve may be set for equal lead by the 
following method. 

Loosen the eccentric on the shaft, and turn it around till it 
gives the maximum port-opening first at one end and then at 
the other. If the maximum port-openings are not equal, make 
them so by changing the length of the valve-spindle by half the 
difference; this operation adjusts the length of the valve-spindle. 
When that adjustment is complete, set the engine on a dead-point 
and give the valve the proper lead by turning the eccentric on the 
shaft; this adjusts the angular advance. This method is con- 
venient when it is difficult to turn the engine. 

Valves which do not have harmonic motion cannot be so set; 
as examples, may be quoted a slide- valve having equal lead and 
with the cut-off equalized by aid of a rocker or bell-crank lever, 
and a valve controlled by a link-motion or a radial valve-gear; 
the two last forms will be described in future chapters. 

To set a valve for equal cut-off. — With the crank on the head- 
end dead-point, give the eccentric the proper angular advance, 
and give the valve the proper lead. Move the engine forward 
till cut-off occurs, and measure the displacement of the cross-head 
from the beginning of the stroke. Move the engine forward, 
again, till cut-off occurs on the return stroke, and measure the 
displacement of the cross-head from the crank end of the stroke. 



PLAIN SLIDE- FA LVE. 35 

Should the cut-off be earlier at the head end than at the crank 
end the valve-spindle is too long; and conversely it is too short 
if the crank-end or return-stroke cut-off is the earlier. In either 
case, change the length of the valve-spindle by an amount which 
it is estimated will correct the inequality; it may be convenient 
• to draw a valve-diagram to aid in making an estimate for a large 
engine. Set the engine again on the head-end dead-point, and 
adjust the lead by moving the eccentric. Try the cut-off again, 
and repeat till the result is satisfactory. 

It is apparent that a valve that is designed for equal cut-off 
will be properly set if the leads are made what the design gives 
for them. When such information is at hand, the process of 
setting the valve will be the same as the first method except 
that the lead at each end is to be made the proper amount, with 
the addition that the displacement of the cross-head at cut-off 
is to be determined for each stroke, and the adjustment is to 
be completed by the method just given. 

To set a valve with the steam-chest cover on. — It is customary 
to provide for setting certain valves for locomotive engines and 
some other engines, with the steam-chest cover on, and with 
steam up. In preparation the valve is set to give the proper lead 
at one end, as shown by Fig. 2, PI. VIII, a centre-punch mark 
is made at a point on the valve-chest and another mark at a 
point on the valve- spindle, and a tram is made of the proper length 
to reach from mark to mark. The valve is in like manner set to 
give the proper lead at the other end and a second tram is made 
to reach from mark to mark, as indicated by Fig. 3. It is appar- 
ent that after such preparation the valve may be set to give the 
proper leads by aid of the trams when the valve-chest cover is in 
place and the valve itself cannot be seen, and that the valve- 
gear can be set by the first method to give equal leads, or any 
predetermined leads. The description with two trams is given 
because the method is more apparent on the diagrams; in prac- 
tice it is customary to use one tram which is set with one point 



36 VALVE-GEARS FOR STEAM-ENGINES. 

on the valve-chest as in Fig. 2, and the other point of the tram 
determines a point on the valve-spindle which is marked with 
a centre-punch; with the valve in the position shown by Fig. 3. 
the same tram is used to locate another centre-punch mark on 
the valve-spindle; consequently the valve may readily be set to 
give the proper leads by aid of the tram and the two centre-punch 
marks on the valve- spindle when the steam-chest cover is in 
place. 

It should be noted that the method of setting the valve with 
equal lead or equal cut-off insures that the action of the valve 
shall be what is desired when opening or closing. Any error 
of design due to the neglect of the angularity of the eccentric- 
rod is therefore transferred to some other part of the motion 
of the valve, namely, to a place where the valve is open or closed 
and any irregularity of motion is then of little consequence. 

Areas of Steam-pipe and of Steam-ports. — The proper sizes of . 
the steam-pipe and of the ports and passages for an engine are 
determined by comparison with successful engines. For this 
purpose it is customary to make a conventional calculation of 
the velocity of the steam through pipes and passages and to use 
such a conventional velocity for determining the areas of the 
sections of pipes and passages and of steam- and exhaust-ports. 

To find the conventional steam velocity it is assumed that 
the cylinder is filled at each stroke of the engine, or, more prop- 
erly, that the cylinder takes a volume of steam equal to the piston- 
displacement, by which term is understood the volume of a 
cylinder equal in diameter to the engine-cylinder and in length 
to the stroke of the engine. . 

Suppose, for example, that a certain engine having the diam- 
eter of the cylinder 18 inches and the stroke 3 feet, makes 75 
revolutions per minute. The piston displacement will be 



w /i8\ 2 



30 cubic feet, 



PLAIN SLIDE-VALVE. 37 

and the volume of steam assumed to be used by the engine per 
minute will be 

2 X 75 x 5-3°— 795 cubic feet. 
If the steam-pipe has a diameter of 5 inches, its area will be 
about 



*?(£'-"* 



4 

of a square foot, so that the conventional steam velocity will be 
795 -r- 0.1 36 = 6000 — 

feet per minute. 

We may now use this velocity to calculate the steam-pipe 
and the ports and passages. 

For example: The diameter of the steam-pipe of an engine 
having a diameter of 18 inches and a stroke of 3 feet, and mak- 
ing 75 revolutions per minute, should be five inches as deter- 
mined by the following calculation. 

The piston-displacement is 



* x(^) 2 

4 \I2/ 



, X3 = 5.30 cubic feet; 

4 \I2/ 

the volume of steam per minute is 

2X75X5.30 =795 cubic feet; 

and the area of the steam-pipe to give a velocity of 6000 feet 
per minute should be 

s\%\ X 144 = 1 9.08 square inches; 

so that the diameter should be 

\i 



(^Xio.og) 1 



=4-93' 
or very nearly 5 inches. 



L. 



38 VALVE-GEARS FOR STEAM-ENGINES. 

It is only with small and slow engines that a velocity as low 
as 6000 feet a minute will be found. Velocities as high as 
8000 and 10,000 are common, and 12,000 feet per minute is not 
infrequent. 

If the steam-pipe has considerable length, a small diameter 
with high velocity is to be avoided, if possible, to avoid excessive 
loss of pressure. If the diameter is smaller than advisable, it 
will be expedient to place a steam-drum near the engine, espe- 
cially if the engine has a short cut-off. 

The areas of ports and passages leading to the cylinder should 
be equal to that of the steam -pipe; and the areas of ports and 
passages leading from the cylinder should be double that area; 
a port or passage for both supply and exhaust is to be calculated 
for the latter. In some cases it is more difficult to provide suffi- 
cient areas for ports and passages than for the steam-pipe. 

For example: The engine mentioned above should have the 
area of the port. 

2X19.08 = 38.16 square inches. 

Now, it is seldom possible to make the transverse length of 
the port equal to the diameter of the cylinder; -fo of the diameter 
is not unusual. Using this proportion, the width of port will be 

38.16-^14 = 2.65 inches. 

This calculation is made with the conventional velocity of 
6000 feet per minute. Were the velocity taken at 12,000 feet 
per minute, the width would, of course, be half as much, namely, 
if inches. 

When it becomes difficult or undesirable to give the slide- 
valve sufficient motion to open the steam-port wide for the sup- 
ply, the maximum port-opening may be made from A to T V the 
width of the port. 



PLAIN SLIDE-VALVE. 39 

When special valve- gears are used that open the valve rapidly 
and close it promptly, the area of the ports and passages may be 
made smaller than the above methods provide, but such reduc- 
tion should be made only with complete knowledge of the action 
of the valve and of the effect of the reduction on the flow of steam. 



CHAPTER II. 
ADJUSTABLE ECCENTRICS. 

Reversing with Loose Eccentric. — The device shown by Fig. 
4, PI. VIII, was used for reversing some of the earliest locomo- 
tive and marine engines; it is to-day used for reversing small 
and unimportant engines, and, with some modifications to secure 
positive action, is used on engines of considerable power. As 
shown, the crank is at C, and the eccentric has its centre at E, 
so that the engine will run in right-handed rotation as shown by 
the arrow. The eccentric is loose on the shaft and has a pin at 
B, which engages with the end of a circular slot in a disk back of 
the eccentric, so that the eccentric is driven by the disk. To 
reverse the engine, it is stopped, and the eccentric or the engine 
is turned till the pin B engages with the other end of the slot 
at£'. 

The valve-circles for forward and for backward motion are 
drawn at OP and OP', and the lap-circle is nn x n 2 ; the cut-off 
occurs at OR, on the forward stroke when running right-handed, 
and at OB!, on the forward stroke when running reversed. 

In this chapter the engine-shaft is assumed to be located to 
the right of the cylinder and the crank in forward motion turns 
to the right, consequently the valve-circles come to the left of the 
vertical YY', as shown in Fig. 4. This disposition has been 
chosen deliberately, so that the student may become familiar with 
both arrangements. The valve-circles for showing the other 
half travel of the valve are omitted to avoid confusing the diagram. 

40 



ADJUSTABLE ECCENTRICS. 4 1 

Shaft-governor. — At the present time a large number of 
engines of comparatively small power and high rotative speed 
are controlled by shaft-governors, which act directly on the valve 
of the engine. Fig. 1, PL XI, shows such a fly-wheel governor, 
which was formerly used on the straight-line engine. It is desir- 
able for illustration because its parts are clearly distinguishable 
and because its action is easily understood. XX' is the centre- 
line of the cylinder, which lies to the left, and xod is the line of 
the valve-spindle, which is moved by a shifting eccentric through 
the bent rocker CTa, designed by the method of page 25 to give 
equal cut-off and equal leads. The consequence is that when the 
crank is at C ready for the return stroke in right-handed rota- 
tion, the eccentric is at E and the centre-line to which the motion 
of the eccentric and eccentric-rod is referred is OS, making an 
angle SOX with the centre-line of the cylinder. As explained 
in connection with the discussion of the rocker, this peculiarity 
of the drawing of Plate XI is of importance in the design of the 
rocker and is not taken into account in the design of the valve; 
neither need it be taken into account in the explanation of the 
action of the fly-wheel governor, which would act in exactly the 
same way if there were no rocker and if the two lines XX' and 
OS coincided. 

The essential parts of the governor are the weight W and the 
spring QL. The weight W moves at the end of the lever WNM, 
which is pivoted at N to one of the arms of the fly-wheel; the 
spring QL, (which is in compression), pushes through the bars LV 
and VM against the end M of the lever and tends to force the weight 
W toward the centre of the wheel. The eccentric is cast on to 
a diamond-shaped plate SV, which is pivoted at S to the hub of 
the fly-wheel and is pinned to the bar LV and VM at V. When 
the engine turns slowly, the weight W is pressed against the hub 
of the fly-wheel and the valve acts like a plain slide-valve with a 
fixed eccentric, ^giving a long cut-off; when the engine approaches 
its normal speed the centrifugal force of the weight W overcomes 



42 VALVE-GEARS FOR STEAM-ENGINES. 

the tension of the spring and the ball moves out from the hub 
and shifts the centre of the eccentric toward the shaft in such a 
way as to shorten the cut-off in a manner to be discussed later. 
It is to be borne in mind that the pivot S, the diamond plate SV, 
the weight W, the lever WM, the rods MV and VL, and the 
spring QL are all attached to the fly-wheel and revolve with it, 
usually at such a speed that they cannot be distinguished while 
the engine is running. 

Suppose that while the engine is running at a certain speed 
with the weight W at a given distance from the shaft, the load on 
the engine is reduced; the effort which the steam at the given 
setting of the valve can exert, will be greater than necessary to do 
the work and the excess will be applied to increasing the speed 
of the engine, and in consequence the centrifugal force of the 
weight W will enable it to move out further, compressing the 
spring QL and forcing the eccentric toward the shaft, thus short- 
ening the cut-off and adjusting the work of the engine to its load. 
Of course a contrary action will take place when the load on the 
engine is increased. It must be noted that the engine will always 
increase in speed as the load is reduced, so that the governor 
does not keep the engine at constant speed, but, rather, it restrains 
the variation of speed within certain predetermined limits. 

The defect of all the earlier fly-wheel governors, like the one 
illustrated, was their tendency to shift the valve-gear too suddenly 
and too far if a sudden change of load occurred ; the consequence 
was that the engine after such a change of load would slow down 
and speed up alternately for some time before it would settle 
down to the new conditions of service. To overcome this tend- 
ency inertia-governors have been devised with heavy moving- 
parts so hung that the centrifugal force increases but a moderate 
amount when the parts shift to adapt the work to the load. 
The increase of centrifugal force must move the heavy parts in 
order to shift the valve-gear and consequently violent fluctuations 
of cut-off are restrained, while at the same time the entire gear 



ADJUSTABLE ECCENTRICS. 43 

can be so constructed as to avoid friction and be sensitive to 
small changes of load or steam-pressure. 

In order that a shaft-governor may be able to control the 
valve of an engine, and maintain nearly uniform speed without 
being excessively large, the valve must be nicely balanced and 
must move freely. For this purpose it is customary to use piston- 
valves without packing rings; or if rings are used they are set 
at a determined diameter. Sometimes the packing- rings are 
transferred to the valve-seat and can be adjusted to the valve. 
If a flat valve is used, it is made double-faced, and runs between a 
fixed seat and a parallel plate or adjustable outside seat, so that 
it acts much like a piston-valve. Preferably the valve should 
take steam in the middle so that the valve-spindle shall run in 
exhaust-steam and be easier to keep tight without excessive 
pressure on the packing. 

Shifting Eccentric with Variable Lead. — A shifting eccentric, 
like that shown by Fig. 1, PI. X, may be used for reversing an 
engine, and it possesses also the property of giving a variable 
cut-off. The eccentric is swung on a pivot (located at S on the 
diagram) which is carried by an arm keyed to the shaft, and it 
is slotted to clear the shaft; the angle OSO' is made equal to 
ESE', so that the centre of the eccentric may be brought to the 
point E' when the engine is reversed. Let the lap of the valve 
be equal to Ob; then the displacement of the valve when the 
engine is on a dead-point is Oa, found by drawing the vertical 
EaE' , and the lead is ha. 

In Fig. 2 the valve-circle OP represents the valve-motion 
when the eccentric-centre is at E. The cut-off occurs at the 
crank-position OR, or at the piston-displacement xa, assuming 
harmonic motion ; with crank and connecting-rod the piston- 
displacement will be longer at the forward-stroke cut-off, and 
shorter at the return-stroke cut-off, but in such case xa is nearly 
the mean for the two strokes. When reversed the motion of 
the valve will be represented by the dotted valve-circle OP'. 



44 VALVE-GEARS FOR STEAM-ENGINES. 

Suppose, now, that the eccentric-centre is shifted to Ei, Fig. 
i; the angular advance is YOEi, and the eccentricity is OEi. 
The valve-circle OP\ will represent the motion of the valve; it 
has the angle YOPi equal to the angular advance, and the 
diameter OP\ equal to the eccentricity when the eccentric -circle 
is at Ei, Fig. i. The point P x is evidently on an arc of a centre 
having its centre on XOX' produced, and drawn with a radius 
equal to ES, Fig. i. In like manner the valve-circles OP 2 and 
OPo represent the motion given to the valve when the centre 
of the eccentric is at £2 and at E , respectively. The piston - 
displacement at cut-off for the valve-circle OP\ is xa\ ; the cut-off 
for the valve-circle OP2 is at a%, and for the valve-circle OPo 
is at a . Thus it appears that the cut-off may be made to vary 
from the piston-displacement xa to the piston-displacement xa ; 
that is, from f to £ of the stroke. All the other events of the 
stroke, namely, compression, release and admission, vary at the 
same time as the cut-off, and in a similar manner, though to a 
less degree. Of these other events, the admission varies the least ; 
an examination of the figure will show that the lead-angle increases 
from about 2 to about 40° The lead increases from ha to bE , 
Fig. 1, and the increase is as clearly shown by Fig. 2. An arc 
representing the exhaust-lap would, if drawn, show the change 
of release and compression; it is omitted to avoid further com- 
plexity. Such an arc would show that the compression varies 
less than the cut-off, and that the release varies more than the 
admission. It is apparent that the increase of the lead depends 
on the radius SE (Fig. 1) of the arc on which the eccentric- 
centre moves, and may be diminished by moving the pivot S 
away from the axis of the shaft. 

The gear is said to be in full-gear forward when the eccen- 
tric is at OE, Fig. 1, and at full-gear backing when the eccen- 
tric is at OE'. When the eccentric is at OEq the gear is said 
to be at mid-gear; intermediate positions may be called grades. 
An examination of Fig. 2 will show that, since the centre of the 



ADJUSTABLE ECCENTRICS. 45 

valve-circle OPo, is on the axis XOX', the crank-angle at admis- 
sion is equal to the crank-angle at cut-off, and this, with other 
considerations, will indicate that the mid-gear position of the 
eccentric does not give proper motion of the valve for either 
forward or backward motion of the engine. 

Fig. 2, Plate XI, gives the valve- diagrams for the eccentric 
controlled by the shaft-governor shown by Fig. i, but drawn 
to eight times as large a scale. Since this engine always runs in 
the same direction, only one set of valve-diagrams is drawn 
(above the axis XX'), and the eccentric is slotted only enough 
to allow for a corresponding shifting of the eccentric. 

The action of the reciprocating parts of a high-speed engine 
is of great importance. A considerable part of the work of 
the steam is expended in imparting motion to the reciprocating 
parts during the first half of the stroke, and this stored energy 
is restored during the second half of the stroke, as the recipro- 
cating parts come to rest. In order that they may come to rest 
quietly at the end of the stroke, the piston should be cushioned 
by compression. Now, a valve that gives a variable cut-off 
and a variable compression is likely to have too little com- 
pression at full-gear and too much at short cut-off. An engine 
with a large clearance will suffer less from this difficulty than one 
with a small clearance; consequently the clearance of high- 
speed engines with shaft -governors is often made large, but a 
large clearance is not conducive to economy in the use of steam. 
Now, lead may act like compression, to stop the reciprocating 
parts, so that in general the more compression an engine has the 
less lead it may need. But it has just been seen that the shift- 
ing eccentric, shown on Plate X, gives an increasing lead toward 
mid-gear, that is, at the time when it may be least needed on a 
stationary engine. Had the pivot S been placed on the opposite 
side of the shaft, then the lead would have decreased toward 
mid-gear. Fig. i, PI. XII, gives the valve-diagrams for such an 
eccentric. 



46 VALVE-GEARS FOR STEAM-ENGINES. 

Shifting Eccentric with Constant Lead. — Fig. 2, PL XII, 
shows an eccentric that has a motion square across the shaft, 
thus carrying the centre of the eccentric on the straight line 
EEqE' from full-gear forward to full-gear backing. It is at once 
apparent that the lead is constant. Fig. 3 gives the valve- 
diagrams for the full-gear, mid-gear, and two intermediate 
grades. Though the lead is constant, the lead-angle is not so; 
a comparison with Fig. 2, PL X, will show that the variation 
of the lead-angle is not so much as that for an eccentric with 
increasing lead, but it is more than for an eccentric with de- 
creasing lead, as may be seen by a comparison with Fig. 1, 
PL XII. 

A shifting eccentric with constant lead must be slotted to 
clear the shaft; the line 00' is made equal to EE f , in order 
that E may pass to E' when the engine is reversed. If the 
engine runs always in one direction, the slot, from centre to 
centre, may be only as long as EE . 

The mechanism for guiding a shifting eccentric along a straight 
line is more complicated than that for guiding such an eccentric 
on the arc of a circle and consequently that form has been but 
little used. 

The shifting eccentric accomplishes nearly the same result 
as the link-motion, to be described in the next chapter, but with 
fewer parts and by a more evident action; it is consequently 
desirable that it shall be clearly understood before beginning 
that chapter. 



CHAPTER III. 

LINK-MOTION. 

The valves of locomotives, marine engines, and other re- 
versing engines are commonly controlled by a mechanism 
called a link-motion; this mechanism has also the property 
of giving a variable cut-off. The mechanism consists essen- 
tially of two eccentrics, one for full-gear forward and one for 
full-gear backing, together with the eccentric-rods and the link. 
The eccentric-rods are attached to the link, at or near the ends, 
and the link is slotted or otherwise arranged to receive a block 
on the end of the valve-spindle, or a radius-rod, or on the end of 
a rocker, as the case may be. The link-motion takes two forms ; 
in one, known as the Stevenson or shifting link, the link is 
moved on the block to reverse the engine or to vary the cut-off; 
in the other, known as the Gooch or stationary link, the block 
is moved in the link to accomplish the same object. 

Stephenson Link. — The usual form of link-motion for Ameri- 
can locomotives is shown by Figs, i and 2, PL XIII. The valve 
is moved through a rocker so that the eccentrics follow the crank; 
thus, the centre of the crank-pin is at C, and the go-ahead eccen- 
tric has its centre at E, while the backing eccentric-centre is at 
E'. The link-pins P and P', to which the eccentric-rods are 
attached, are set back from the link-arc, and the link may move 
over the link-block B so far as to bring the centre of the block 
opposite the centre of the link-pin, as shown by Fig. 1 ; in which 
position the motion of the valve is controlled almost entirely by 

47 



L 



48 VALVE-GEARS FOR STEAM-ENGINES. 

the eccentric E, and has essentially the motion of a plain slide- 
valve. The link is suspended by a link or hanger, nm , from a 
reverse-shaft centred at S; the hanger takes hold of the saddle- 
pin m on a plate that is commonly at the middle of the link. 

A locomotive has two cylinders, with pistons acting on two 
cranks set at a right angle, and thus has two engines each of 
which must be provided with its own link-motion. Both links 
are suspended from one reverse-shaft, which has an arm SR 
from which a rod runs to a reverse-lever conveniently located 
in the engineer's cab. The reverse-lever moves over a notched 
arc, and by aid of a latch engaging with the notches the link 
may be set and secured in any desired position. 

Fig. 2, PL XIII, gives an end elevation of the link, the 
hanger, and one arm of the rocker carrying the link-block B. 

English locomotives commonly have the link acting directly 
on the • valve-spindle, without the intervention of a rocker. In 
such case the link-pins should be placed on the link-arc, as 
shown by Fig. 3, PL XIII, and with that construction the link- 
block cannot be opposite one of the link-pins and cannot receive 
the full motion of the eccentric. Consequently the eccentricity, 
and with it all the dimentions of the link-motion, must be larger 
to give proper motion to the valve. 

The link-motion for the high-pressure cylinder of one of 
the engines of the U. S. S. Maine is shown by the figures on 
Plate XIV. The parts are lettered as on Plate XIII, and, 
although no rocker is used, the eccentrics follow the crank, 
as the valve takes steam in the middle ; thus E and E' are 
the centres of the eccentrics, and P and P' are the link-pins, 
which in this case are on the link- arc; 6 1 is the reverse- shaft, 
and NP is the drag-link or bridle which takes hold of the 
go-ahead link-pin. The link, which is known as the Scotch or 
side-bar link, is shown in plan by Fig. 2. The link-block is 
between the side- bars, and is pivoted directly on the end of the 
valve- spindle; thus the link can be set so that the axis of the 



LINK-MOTION. 49 

link-pin coincides with that of the link-block pivot, and the 
full motion of the eccentric can be given to the valve. The 
head of the valve-spindle is guided by cast-iron jaws, as shown 
in Fig. i. The end of the reverse-arm is slotted and provided 
with a sliding-block, screw and hand-wheel, as shown, so that 
the cut-off may be adjusted in a manner to be described later. 

Open Rods and Crossed Rods. — If the eccentric-rods of a 
link-motion are connected as shown in Fig. i, PI. XV, the 
rods are said to be open; on the other hand, the rods are said 
to be crossed when connected as shown by Fig. 2. In both 
figures the crank is on the crank-end dead-point, and the valve- 
gear has no rocker. A link-motion with a rocker is said to 
have open rods when the eccentric-rods are connected as shown 
by Fig. 3; aTb is the rocker, and be the valve-spindle; the crank 
is on the head-end dead-point. If the link-motion moves a 
piston- valve which takes steam in the middle it will have open 
rods when the parts have the relation of Fig. 3, without a rocker. 
In all these figures the link-pins are on the link-arc. Since half a 
revolution will apparently cross the rods for Figs. 1 and 3, while it 
will apparently open the rods for Fig. 2, the nomenclature seems to 
be unfortunate. There is, however, a real difference in the meth- 
ods of the connection of the rods, and that difference has an impor- 
tant influence on the action of the valve, for open rods give an 
increasing lead from full toward mid gear, while crossed rods 
give a decreasing lead from full toward mid gear. All arrange- 
ments which give increasing lead toward mid-gear are classed with 
open rods. In Fig. 1, the full lines Ep , E'pd, and the arc popo,' 
show the eccentric-rods and the arc of the link at mid-gear, while the 
thin lines Ec, E' ft , and the arc eft, show them at full-gear forward. 
Since the valve and valve-rod have the same motion as the link- 
block, it will be sufficient to trace the motion of the latter. At full- 
gear the link-block will be at c, found by intersecting the line of 
centres with E as a centre, and with a radius equal to the length 
of the eccentric-rod. The eccentric-pin ft is located by draw- 



5° VALVE-GEARS FOR STEAM-ENGINES. 

ing arcs from E' and c, with the lengths of the eccentric-rod 
and the length of the link as radii. At mid-gear the link-block 
is at c ; the points po and pd are at a distance from the centre- 
line OX, equal to half the chord of the link-arc, and the link 
is erect. The increase of lead from full-gear to mid-gear, cc Q , is 
apparent from the diagram. A similar construction in Fig. 
2 shows the decrease of lead from full-gear toward mid-gear for 
crossed rods. In the figure the decrease is greater than the full- 
gear lead, so that the valve is shut at the dead-point when the 
link is at mid-gear. 

Long and Short Rods. — The variation of lead from full- 
gear toward mid-gear is due to the curvature of the link-arc, 
and is more pronounced for a link with short radius than for one 
with long radius; now the radius of the link-arc is usually equal 
to the length of the eccentric-rod, hence the variation is more for 
short than for long rods. In Fig. i, PI. XV, it is apparent that 
c"cq" is greater than ccq\ a similar construction will show that 
the decrease of the lead from full-gear to mid-gear for crossed 
rods is more marked for short than for long rods. 

. Radius of the Link-arc. — An analytical discussion (see Appen- 
dix) of the link-motion shows that the radius of the link-arc 
should be equal to the length of the eccentric-rod; if the link- 
pins are on the link-arc, then the radius should be the distance 
from the centre of the eccentric to the link-pin; but if the pins 
are back of the arc, the radius is the distance from the centre of 
the eccentric to the link-arc, i.e., the length of the rod plus the 
distance the pins are back of the arc. The same discussion estab- 
lishes also the fact that open rods give increasing lead, and that 
crossed rods give decreasing lead, from full-gear toward mid-gear; 
but the demonstrations given are believed to be useful, and a sim- 
ilar demonstration will be given of the proper radius for the arc. 
In Fig. i, PI. XV, the link-block is at c at full-gear when 
the crank is on the crank-end dead-point; when the crank is 
on the head-end dead-point a similar construction will give for 



Cn 






LINK-MOTION. 



the position of the link-block the point c' . The point o, half- 
way between c and c', corresponds to the mid-position of the 
valve, and from o the lap on, on' may be laid off on each side, 
giving nc=n'c' for the lead. At mid-gear the head-end lead 
is nco, and a similar construction for the crank-end dead-point 
will give n'co=nco for the crank-end mid-gear lead. If now 
a diagram is drawn for some intermediate gear of the link, it 
will be found that the lead is the same at the two ends, and that 
it is intermediate between nc and nco. Fig. i is drawn with 
the radius of the link-arc equal to the length of the eccentric- 
rod, and any diagram drawn with dimensions chosen at random 
will in like manner show equal leads under like conditions. 
Constructions for a link with crossed rods will also show equal 
leads if the radius of the link-arc is equal to the length of the 
f eccentric-rod. Consequently, it may be inferred that the one 
requirement for equal leads is that given, i.e., that the radius 
of the link-arc shall be equal to the length of the eccentric-rods. 
A natural inference is that any other radius for the link-arc will 
give unequal leads for some grades of the link, and such will be 
found to be the case if constructions are made. 

Zeuner's Diagram. — The best idea of the nature of the motion 
given by a link to a valve is obtained by drawing a series of valve- 
diagrams like those for a shifting eccentric. An analytical proof 
that such diagrams properly represent the motion of the valve 
will be found in the appendix. An approximate construction 
sufficient for the purpose can be made in the following manner. 
First draw a diagram like Fig. i, PI. XV, showing the link 
full-gear and in mid-gear and measure the difference in lead in 
these two positions. Next draw a pair of axes, XOX r and OY, 
as in Fig. 4, PL XVI, and draw the full-gear valve-circle OP. 
Drop the perpendicular Pq onto the axis XX' and draw the 
lap-arc nn" with the proper full-gear lead, qn. Lay off the increase 
of lead qP , as determined from Fig. 1, PL XV, and with a centre 
on the axis XX', draw an arc through P and Pq. Choose a 



52 VALVE-GEARS FOR STEAM-ENGINES. 

point like Pi on this arc and draw the line OP x and on it the 
valve- circle OP\\ it will exhibit the action of the valve for the 
corresponding intermediate grade of the link. A number of 
important facts concerning the general action of a valve controlled 
by a link-motion can be inferred directly from such a diagram. 
If R0R1R be taken to represent the path of the crank (drawn to 
a different scale), then the mean piston-displacement at cut-off for 
full-gear is xa, about ||- of the stroke. For the grade OP x the 
piston-position at cut-off will be xa x , somewhat more than | of the 
stroke, but the maximum port-opening decreases to less than half 
that at full-gear, while the lead is nearly as much as at mid-gear. 
The grade represented by OP 2 gives cut-off just before half- 
stroke and a port-opening less than a quarter as much as at full- 
gear. These two features, the increase of lead and decrease of 
port-opening are the most striking features of the action of a 
valve which is controlled by a link-motion with open rods. A 
link-motion with crossed rods will, of course, show a decreasing 
lead toward mid-gear, but it will have much the same notable 
decrease of port-opening. 

If a diagram like Fig. 4, PI. XVI, is drawn, but with a larger 
angular advance and larger steam-lap, it will show a better port- 
opening at an early cut-off, but the maximum cut-off corresponding 
to full-gear of the link will be correspondingly reduced. A 
careful study of such diagrams will give a broader and clearer 
idea of the essential properties of the link-motion than any work 
with a model or with complete diagrams of the gear. Unfor- 
tunately the inequalities which it is customary and desirable to 
introduce into the valve-motion by the way the link is suspended, 
make it impossible to design a link-motion by such diagrams alone; 
the complete design can be best made by aid of a skeleton wooden 
model to be described on page 64. 

Gooch Link. — Fig. 1, PL XVIII, shows the Gooch or sta- 
tionary link, as applied to locomotive engines. E and E' are 
the forward and backing eccentrics, from which the eccentric 



LINK-MOTION. 53 

rods lead to the link-pins P and P' . The link is suspended by 
the rod mn, from a fixed pivot n, and has its convex side turned 
toward the axle O. The link-block B is carried by a radius- 
rod BD, which is connected directly to the head of the valve- 
spindle at D. By means of a reverse-arm ST and hanger TU, 
the engineer may place the link-block B opposite the link-pin 
P for full-gear forward, opposite the link-pin P' for full-gear 
backing, or at any intermediate position. The action of this 
link-motion is therefore equivalent to that of the Stephenson 
link-motion. The details of the mechanism are varied some- 
what by different makers. In the figure the link is suspended 
from a saddle-pin on or near the chord joining the ends of the 
link-arc; and for this purpose a plate or bridge similar to that 
shown by Fig. 2, PL XIII, is employed which permits the passage 
of the link-block. The saddle-pin is sometimes placed behind 
the link-arc toward O, so as to avoid the use of a plate or bridge. 
The link-pins are placed behind the link-arc to allow the link- 
block to be brought opposite the link-pins. They may be placed 
on the link-arc, using a link like that shown by Fig. 3, PL XIII, 
but turned so that the convex side is toward the axle O; in which 
case the full action of the eccentric cannot be given to the valve. 
Sometimes a box-link, shown by Fig. 3, PL XVIII, is used, 
and then the saddle-pin and link-pins may be placed in any 
desired positions without interfering with the link-block; this 
device is equivalent to the side-bar link shown on Plate XIV. 

Open and Crossed Rods. — As was found to be the case with 
the Stephenson link, the rods of the Gooch link may be open 
or crossed. Fig. 1, PL XVIII, has open rods, and Fig. 2, PL 
XVII, has crossed rods. 

Radius of the Link-arc. — The common and proper practice 
is to make the radius of the link-arc equal to the length of the 
radius-rod; and when so made the lead is constant for all grades 
of the link. This property is at once evident from inspection 
of Fig. 1, PL XVIII, and Fig. 2, PL XVII, one having open and 



54 VALVE-GEARS FOR STEAM-ENGINES. 

the other crossed rods; for it will be seen that when the engine 
is at a dead-point and the link is erect, the link-block may be 
moved from one end of the link-arc to the other without moving 
the valve. 

Comparison of the Stephenson and Gooch Links. — A com- 
parison of the link-motions on Plates XIII and XIV with that 
on Plate XVIII will show that the Gooch link-motion has more 
parts and more joints at which lost motion will result from wear, 
and that it occupies nearly twice the longitudinal space required 
for a Stephenson link-motion. As an offset may be urged its 
property of giving a constant lead. The choice of a link-motion 
for a specific purpose must depend on the importance that should 
be attached to any given feature of the gear under the given 
conditions. With proper proportions either gear can be made 
to give the valve a nearly harmonic motion, or, with proper 
modifications, either gear may be adjusted to give an equalized 
cut-off; from this point of view neither appears to have an ad- 
vantage. 

Locomotive Link-motion. — Reversing engines are of two 
types, locomotive engines and marine engines; the conditions 
of their service are so different as to merit detailed discussion. 
Some stationary engines are reversing engines, and are controlled 
by hand instead of by a governor; for examples may be men- 
tioned winding and hoisting engines, and engines for driving 
reversing roll-trains. According to the conditions of their use 
they will fall into one or other of the two classes mentioned, or 
may partake of the characteristics of both. 

In starting a railway train, the link-motion is thrown into 
full-gear forwards, and should then give a long cut-off, so that, 
with the throttle- valve partially open, a moderate and steady 
force may be exerted on the driving-wheels to overcome the 
friction of, and impart motion to, the train, without slipping 
the wheels on the track. The lead may properly be small at 
full-gear, and is sometimes zero or even negative. As the train 



LINK-MOTION. 55 

gets under way and the revolutions per minute become high, 
the action of the reciprocating parts becomes important; just 
as was seen to be the case for a high-speed stationary engine 
(see page 45), there must be a considerable amount of compres- 
sion in order that the engine may run smoothly. An early ad- 
mission and release are also desirable in order that the steam 
may be supplied and exhausted freely. All these conditions 
are met by raising the Stephenson link toward mid-gear and 
opening the throttle-valve, and at the same time the economic 
advantage of the expansive working of steam can be obtained. 

American and English locomotive-designers have used the 
Stephenson link-motion, while Continental designers have used 
the Gooch link quite widely. In American practice the cylin- 
ders are commonly placed outside of the locomotive-frames, 
with the valve-chest on top; the link-motions are placed be- 
tween the frames and act on the valve through a rocker, as 
has already been shown on Plate XIII. English locomotives 
frequently have the cylinders inside the frames, and the valve- 
chests are on the sides of the cylinders and under the smoke- 
box; the link-motions then act directly on the valve-spindle, 
using a link like that shown by Fig. 3, Plate XIII. When the 
Continental locomotive designers use the Gooch link-motion, 
they place it outside the drivers, and so readily find room for 
eccentric-rods and radius-rod. Such a disposal of the valve- 
gear keeps it in sight where it may receive attention, but does 
not meet with favor among American and English engineers, 
since it is liable to derangement from slight accidents. 

Locomotive link-motions have the pins and other smaller 
wearing parts made of hard steel, the link is case-hardened, 
and the eccentric-rods are bushed with steel; the eccentrics 
and straps are the only exception to the rule that all the wear- 
ing parts are made as hard as possible. With the exception of 
the eccentric-straps, no provision is made for taking up wear; 
when the looseness becomes excessive the whole gear is over- 



56 VALVE-GEARS FOR STEAM-ENGINES. 

hauled, and new pins and bushings provided if necessary. The 
reason for this practice is twofold: first, the complication of 
adjustable parts is avoided; second, the gear is unavoidably 
exposed to dirt and grit, and when grit gets into a joint between 
a hard and a soft metal, it becomes embedded in the latter and 
rapidly abrades the hard surface. The custom is to equalize 
the cut-off by a method that gives a good deal of slipping of 
the block in the link, but as both link and block are hard, and 
the cut-off is continually varying, this practice is not so ob- 
jectionable as it would be on a marine-engine link-motion. 

Marine Link-motions. — At the present time marine engines are 
commonly compound or triple-expansion, and the link-motions 
are used only for reversing the engine, the reverse-arc having 
only three notches, full-gear forward, full-gear backing, and mid- 
gear. Crossed rods may be used to advantage, for then the engine 
can be stopped by setting the link at mid-gear. In this con- 
nection it may be remarked that an engine controlled by a 
Stephenson link-motion with open rods will not necessarily stop 
when the link is placed in mid-gear, provided the engine is run- 
ning under no load or a very light load ; though the engine will not 
start with the link in that position. The normal condition for a 
marine engine is to run at full speed and under a full load, and 
when the speed decreases the load falls off rapidly. The result of 
an attempt to adjust the steam-supply to a smaller load, by 
shifting the link toward mid-gear, is to give an excessive com- 
pression, and an early release, when the reciprocating parts have 
least effect, and when the reduced quantity of steam is readily 
exhausted. Simple-expansion engines and many compound en- 
gines were provided with an independent cut-off valve on the back 
of the main valve, of a type to be discussed in Chapter V. 

Marine-engine link-motions are designed to give the re- 
quired cut-off for full load when set at full-gear; as has already 
been said, there is frequently no provision for shortening the cut- 
off as on locomotives. Since the engine is liable to run for days 



LINK-MOTION. 57 

or weeks at full -gear forward, the gear is designed to give very 
little slipping of the block in the link at this position. As the 
gear is large and frequently massive, the complication of making 
the wearing parts adjustable is not objectionable; and as the en- 
gine works in a closed engine-room, there is no reason why grit 
should get into the wearing surfaces, which may therefore be lined 
with soft metal when that is desirable. 

Modification of the Link-motion. — In the analytical discus- 
sion of link-motions it is supposed that the arrangement of 
the parts and the choice of dimensions are such as to give a 
nearly harmonic motion to the valve. In both the Stephenson 
and the Gooch link-motions the link-pins are supposed to be on 
the link-arc; in the first the radius of the link-arc is assumed to 
be equal to the length of the eccentric-rod, and in the second it 
is assumed to be equal to the length of the radius-rod. It is, how- 
ever, possible, by modifying some of the arrangements, to obtain 
certain desired effects, such as the equalization of the cut-off, 
without sacrificing the equality of the leads. The effect of some 
of the modifications can be proved, or at least inferred, from the 
diagram of the link-motion; but since they are in the nature of 
adjustments and must in any case be worked out by trial, it will 
be sufficient to state some of them for the Stephenson link-motion. 

Link-pins. — The link-pins of a Stephenson link-motion with 
a rocker may advantageously be placed back of the link-arc; 
without a rocker they should be on the link-arc, or they may be 
placed ahead of the arc if mechanical difficulties do not interfere. 

Saddle-pin. — By proper location of the saddle-pin, or the 
point of the attachment of the hanger or bridle, it is possible to 
equalize the cut-off at any point of the stroke both in forward 
and backing gears. This element of link-motion is by far the most 
effective, for good or evil, of all that the designer has at his con- 
trol, and fortunately he usually has complete control over it. 
If a symmetrical gear is desired, the saddle-pin should be placed 
at the middle of the length of the link; with a rocker it will be 



58 VALVE-GEARS FOR STEAM-ENGINES. 

back of the link-arc, and without a rocker it will be ahead of the 
link-arc. With proportions common for American locomotives a 
fair action may be had by placing the saddle-pin at the middle of the 
link and one-third way from the chord to the arc. On such loco- 
motives, with a rocker, the slip of the link-block is greater in for- 
ward than in backing gear, when the saddle-pin is at the middle 
of the link; and the forward-gear slip may be diminished by 
placing it nearer the forward-gear link-pin, but this is attained 
at the expense of the symmetry of the gear. Sometimes the link 
is supported from below instead of being suspended from above; 
and in such case the forward-gear slip is less than the slip in 
backing-gear. Links for marine engines, and in English loco- 
motives without a rocker, are frequently suspended by the forward 
link-pins. It is customary to equalize the cut-off at half- stroke, 
or earlier, by a proper location of the saddle-pin ; an equalization 
at one-third stroke is recommended. 

Reverse-shaft. — The position of the reverse-shaft is often fixed 
or susceptible of but little change. If it can be located at pleasure, 
it may also be used to equalize the cut-off at any point of the stroke. 
When so used, the location of the reverse-shaft is used to equalize 
the cut-off near the end of the stroke, usually in combination 
with an equalization to the cut-off by the location of the saddle-pin 
at half-stroke or earlier. With a rocker, such a manner of 
locating the reverse-shaft is liable to bring it in conflict with the 
eccentric-rods at one of the full-gear positions. 

Radius of the Link-arc.— It has been shown that the link- 
arc for the Stephenson link should have a radius equal to the 
length of the eccentric-rod, in order that the leads may be equal. 
It may sometimes be desirable to use a different radius to facili- 
tate the equalization of the cut-off. Without a rocker the radius 
may be made greater than the length of the eccentric-rod, and 
with a rocker it may be made less. Such a choice of the radius 
of the link-arc will sacrifice the equality of the leads, and the 
deviation from the normal radius must never be enough to badly 



LINK-MOTION. 59 

derange them. In this connection it should be said that the 
lead near mid-gear supplies a large portion of the steam admitted, 
and that the lead at full-gear affects the facility with which the 
engine passes the centres; much inequality in either place is. 
undesirable. With open rods the full-gear lead is small, and 
may vary from a certain amount to double that amount, or to 
zero, without serious consequence. At and near mid-gear the- 
lead is large, and may vary as much absolutely as at full-gear,, 
since that will not be much relatively. 

Any change from the standard radius of link-arc should be 
made by trial with the aid of the model to be described on page 
64. In the use of that model it will be found convenient to start 
with the standard radius and to increase the length of the eccen- 
tric-rods progressively till the desired effect is obtained. After- 
ward the radius of the link-arc may be decreased a like amount 
and a new link-template can be cut and used to determine whether 
the desired results can be attained by using it with the original 
length of eccentric-rods. The reason for this procedure will be 
evident after the model is described, and it will then be evident 
that the length of the rod can be readily varied while a change 
of radius of the link-arc involves the making of a new template. 

The motion of the valve will be more nearly harmonic with 
long rods and with a long link; the first should be twelve times 
and the second four times the eccentricity, or more, except under 
peculiar conditions. A skilful designer may use the inequality 
introduced by short rods or a short link to adjust a link-motion, 
but these dimensions are commonly fixed, and the modification 
of them for that purpose is not in general to be regarded with favor. 

Designing Link-motions. — The design of a link-motion may 
be divided into two parts : first, the choice of such a type of link- 
motion and such general proportions as will be likely to give a 
satisfactory solution of the problem in hand; and, second, the 
application of modifications and adjustments to give equal cut- 
off, or to reduce the slip, or to produce any other desired effect. 



60 VALVE-GEARS FOR STEAM-ENGINES. 

The first part of the design may be much aided by the use of 
the Zeuner diagram; the second part is commonly attained either 
by drawing out the link-motion and by making the proper con- 
structions, or by aid of a working model with adjustable parts. 
A combination of the methods of drawing and using a model, 
combining certain advantages of each, will be explained later. 
The first part of the design is often so fixed by the requirements 
of the general design of the engine, or by custom, that it is liable 
to be neglected. 

Marine-engine Link-motions. — As has already been stated, 
the link-motions of modern marine engines are commonly used 
for reversing only, and not for regulating the power of the engine. 
Since the Stephenson link-motion at full-gear acts like a plain 
slide-valve gear, the determination of the eccentricity and angu- 
lar advance and the design of the valve may be carried out by 
the methods given in the first chapter. It is customary to make 
the head-end lap greater than the crank-end lap, thereby par- 
tially equalizing the cut-off, and the consequent inequality of 
leads (the crank-end lead being the larger) is a partial compen- 
sation for the longer cut-off at the head-end. In Fig. i, PI. V, 
the only change required is to choose the point of cut-off for both 
forward and return strokes, the former being the longer. 

The link is usually guided by the go-ahead pin, as shown on 
Plate XIV and Plate XIX, both of which represent the link- 
motion of the U. S. S. Maine; though sometimes a point beyond 
the link-pin, or a point at the middle of the link, is chosen. This 
particular link-motion actuates a piston-valve like that shown by 
Fig. i, PI. VII, which takes steam in the middle and exhausts at 
the ends. Consequently the motion of the valve is in the oppo- 
site direction from that of a plain slide-valve, and the general 
effect is like that produced by moving a valve through a rocker; 
the eccentric follows the crank, and the rods are crossed, as shown 
on Plate XIV and Plate XIX. Let p and P be the positions of 
the go-ahead link-pin when the crank is on crank-end and head- 



LINK-MOTION. 61 

end dead-points respectively; then with p and P as centres and 
with a radius equal to the length of the bridle, arcs are struck 
intersecting at N, which is one extreme position of the end of 
the reverse-shaft arm. The length of the bridle is such that the 
arc aPpa y nearly coincides with the line XX', and the slipping 
of the link-block is small; the arc aa x is extended both ways for 
sake of clearness in the diagram. 

The location of the reverse-shaft may now be made either 
to give the backing action symmetrical with the forward action 
of the link, or to reduce the slip in backing-gear. 

Symmetrical Action. — Let it be assumed that the backing link- 
pin shall be guided to the points P and p, when the engine is 
on the dead-points; then the go-ahead link-pin will be found at 
Pi and pi. With these points as centres and with the length of 
the bridle for a radius, draw arcs intersecting at n; and with TV 
and n as centres and with the length of the reverse-shaft arm as a 
radius, draw arcs intersecting at S: the last point is the desired 
location of the reverse- shaft. 

Reduction of the Slip. — In full-gear forward the go-ahead 
link-pin moves on the arc aa 1} and the backing link-pin describes 
an elongated looped figure, of which the upper loop is quite 
small; P' and p' are two points on the larger loop. If now 
the link be thrown into full-gear backing, and if the backing 
link-pin be made to move on the line XX', then the go-ahead 
link-pin will describe a looped figure of which Pi and pi are 
two points. To draw the looped figure, let C be a given position 
of the crank, and let E and E' be the corresponding positions 
of the eccentric -centres; with E' as a centre and with the length 
of the eccentric-rod for a radius, cut the line XX' at P; with E 
as a centre and with the same radius draw an arc and intersect 
it with another arc drawn from P and with the length of the link 
between the pins for a radius; then Pi at the intersection of the 
two last arcs is one point on the looped figure. To find other points 
make the same construction for a sufficient number of crank- 



62 VALVE-GEARS FOR STEAM-ENGINES. 

positions, say twelve, at equal intervals around the circle described 
by the crank-pin. 

Find by trial a centre Wo, from which, with a radius equal 
to the length of the bridle, the arc tt\ may be drawn through 
the middle of the looped figure. Then with a radius equal to 
the length of the reverse-arm, draw arcs intersecting at So', this 
is the location of the reverse-shaft for giving as small a slip as 
possible in full-gear backing. With this construction the go- 
ahead link-pin describes the arc tt\ when the link is in full-gear, 
and at the same time the backing link-pin describes a looped 
figure similar to the one at P f p r , and lying partially on one side and 
partially on the other side of the line XX' near Pp. The link- 
block will slip in the link an amount nearly equal to the width of 
the looped figure P\p\, measured on a radial line from n Q ; the 
exact amount of slip can be found by drawing the true looped 
figure near Pp; it is omitted in the diagram to avoid confusion. 
It is evident that the slip of the link-block will be greater if the 
construction for symmetrical action resulting in the location of 
the reverse-shaft at S, should be used. In that case the slip 
is nearly equal to the total deviation of the looped figure P\p\ 
from the arc through P\p\\ it can be found by drawing the true 
looped figure near Pp when the path of the go-ahead link-pin is 
the arc P\p\. 

Adjusting the Cut-off. — The distribution of work among 
the cylinders of a compound or multiple-expansion engine de- 
pends on the ratio of the volumes of the cylinders and on the 
cut-off for the several cylinders. If the distribution of the work 
is not satisfactory when all the links are set at full-gear, it may 
be adjusted, or at any rate it may be improved by shortening the 
cut-off on one or more of the cylinders. On recent marine engines 
which have only three notches on the reverse-arc, namely, full- 
gear forward, full-gear backing, and mid-gear, a device known 
;as a gag is put on the end of the reverse-arm for this purpose. 
The rod of the bridle is carried by a block N (Fig. i, PI. XIV), 



LINK-MOTION. 63 

which may be moved in a slot NM in the end of the reverse- 
shaft arm, by aid of a screw and hand-wheel, and thus the link 
may be moved toward mid-gear and the cut-off may be shortened. 

The construction of the gag for the link-motion shown on 
PL XIV is found on PL XIX. A line (not shown on the diagram) 
is to be drawn midway between nP\ and np\, and perpendicular 
thereto is drawn the line nm ; this is chosen as the centre-line of 
the slot and screw NM, Fig. 1, PL XIV. In full-gear forward 
the centre-line of the slot and screw is at MN, which makes an 
angle of about 7 with a line midway between NP and Np. 
It is apparent that when the block N is moved toward M, 
PL XIV, the cut-off is shortened for forward gear without appre- 
ciably changing the method of supporting the link-motion, while 
in backing gear the cut-off is not affected. This construction is 
commonly found for engines that back only occasionally, but 
for engines, like those for double-ended ferry-boats, which run 
one way as much as the other, it is desirable to shorten the 
cut-off equally in forward and in backing gear. For this pur- 
pose the line of the slot in the gag can be set at NM f and will 
come to nm' in backing gear, the position of those lines being 
found by trial so that the angle which NM' makes with a line 
mid- way between PN and pn, shall be equal to 180 minus the 
angle which nm' makes with a line midway between P x n and 
pin. But this latter construction modifies appreciably the gen- 
eral method of guiding the link and there is likely to result a 
considerable interference with the harmonic motion of the valve. 

Locomotive Link-motions. — In American practice the link- 
motion is set to give equal lead at full-gear, and is adjusted to 
give equal cut-off; the reduction of slip being considered to be 
of less importance, though it is not to be neglected. The ad- 
justment of the cut-off is made by aid of a model with adjustable 
parts, by aid of which an experienced designer can readily work 
out a satisfactory motion, or at any rate as good a motion as 
the conditions will allow. 



64 VALVE-GEARS FOR STEAM-ENGINES. 

In equalizing the cut-off, it is to be borne in mind that any 
irregularity at short cut-off is of much more importance than 
at long cut-off, since the amount of steam admitted to the cylin- 
der is nearly proportional to the length of the cut-off, and the 
work varies with the amount of steam admitted. Thus an 
inequality of half an inch in six inches is xs, while half an inch 
in eighteen inches is only 5 V 

The full-gear or maximum cut-off varies with the condi- 
tions of the service and the judgment of the designer from f 
to H of the stroke. When an engine, for example, one in passen- 
ger service, is to be run at high speed and with a short cut-off, 
it is advisable to make the full-gear cut-off as short as the ready 
handling of the engine, when starting, will permit, in order that 
a favorable action of the valve may be obtained at short cut-off. 
This will be made clear by a comparison of Fig. 4, PI. XVI, in 
which the maximum cut-off is at f of the stroke, with Fig. 1, PI. 
XX, in which the maximum cut-off is at f of the stroke ; the diam- 
eters of the full-gear valve-circles are the same. In each figure OP\ 
is the valve-circle for the link-block half-way between the link- 
pin and the saddle-pin. In Fig. 4, PI. XVI, OP x has a diameter 
of II of an inch, gives a maximum port-opening of M of an 
inch, and the cut-off occurs at 0.70 of the stroke. In Fig. 1, 
PL XX, the cut-off occurs at 0.55 of the stroke, the diameter 
of OPi is iA of an inch, and the maximum port-opening is again 
M of an inch. The comparison also shows the importance of 
the first part of the design of a link-motion, mentioned on page 59, 
and the advantage of using Zeuner's diagram for that purpose. 
Skeleton Model. — The author has found that a skeleton 
model, such as is shown on PI. XX, can be used with advan- 
tage in laying out and adjusting a link-motion. It consists of 
a piece shown by Fig. 3 to represent the crank and eccentrics, 
of a template shown by Fig. 4 to represent the link, and of rods 
to represent the eccentric-rods, the hanger and the reverse-shaft 
arm, together with screws and washers to make attachments. 



LINK-MOTION. 65 

The several parts may be made of any fine-grained hard wood, 
such as mahogany or cherry. Fig. 5 shows one of the joints with 
a thick wooden washer, as at the eccentric-centre e f , Fig. 2. A 
wood screw of proper size is cut off so that it may not protrude 
through the plate into which it is set. The hole at b for the 
screw is drilled a trifle smaller than the shank of the screw at 
the bottom of the threads, and a pointed screw like the one to be 
used is run through to cut a thread in the hole. The hole in 
the washer c may be an easy fit for the screw, while the hole 
in the rod d is a snug fit for the body of the screw under the head. 
The countersunk hole in the rod d should be made with a tool, 
like a machinist's countersink, but with the cutting edges sharper. 
One size of wood screw may be used to fasten all the joints of 
the model, and two drills should be carefully selected, one to 
drill a hole into which the body of the screw will fit snugly, and 
the other to drill a hole in like manner for the shank at the 
bottom of the screw-threads. A steel jig should be made to 
guide the drills and keep them from running to one side while 
drilling the holes in the wooden members of the model. For 
this purpose take a piece of steel, about if inches long, half an 
inch wide, and one-eighth of an inch thick. Draw a line through 
. the middle of the face of the jig and transverse lines about a quarter 
of an inch from each end; continue all lines down the edges of 
the jig to the opposite side to aid in setting the jig. Drill 
holes at the intersection of the longitudinal and transverse lines, 
one for the larger and the other for the smaller drill. Any hole 
for a screw will be located on the member of the template by 
perpendicular lines to which the jig may be set ; after the jig is set 
and clamped in place the hole is to be drilled carefully in a lathe or a 
sensitive drill-press. This method is susceptible of great accuracy 
and delicacy and its success depends in the first place on the ex- 
actness with which the model is laid out and assembled and in the 
second place on the intelligence and skill with which it is used. 
In anticipation of laying out the model, a Zeuner's diagram 



66 VALVE-GEARS FOR STEAM-ENGINES. 

should be drawn as in Fig. i ; in which the full-gear valve-circle 
OP is laid out as for a plain slide-valve to give the lead-angle 
XOA and the cut-off at 0R U corresponding to the piston-posi- 
tion a, on the assumption of harmonic motion. As was found 
to be the case for a plain slide-valve, it may be necessary to 
modify and redraw the full-gear valve-circle in order to get a 
desired lead and lap. The diameter of the mid-gear valve- 
circle may be determined by the graphical method of page 51, 
and then the locus PP 1 P 2 Po of the end of the valve-circle 
diameters may be drawn as the arc of a circle centred on the 
line XX'. 

Laying out the Model. — Experience has shown that the 
model may be laid out and tested very exactly by the following 
method which should be followed explicitly, at any rate for the 
first time. 

To lay out the crank-disk, draw a line AB as nearly as may 
be across the middle of the wooden template used for this pur- 
pose, as indicated on Fig. 1, PL XXa. Lay off the radius of 
the crank-circle from A and thus locate the centre O of the disk 
and draw a line DON through it perpendicular to AB. It will 
be convenient to take this radius as six inches for a full-size con- 
struction, whatever may be the real stroke of the engine. 

At a distance from O equal to the steam- lap plus the full-gear 
lead draw E'H parallel to DN. With O as a centre and with a 
radius equal to the eccentricity describe arcs cutting E'H at E and 
E' respectively; they are the eccentric centres. Draw the lines PS 
and RT through E and E' at right angles to HE' \ they will be 
required for setting the steel jig when the holes are drilled at E 
and E' . Draw the lines OK and OL from O through E and E '. 
Lay the disk flat on a board and with a steel scale square down 
lines to the under side of the disk from A, B, L and K. Drill 
a large hole for the body of the screw at O and small holes for 
the shank of the screw at E and E f . 

To lay out the drawing, stretch a sheet of good drawing-paper, 



LINK-MOTION. 67 

large enough to take the entire construction, or if more con- 
venient stretch two pieces, one for the construction near the crank- 
shaft, and the other for the construction near the link. A full- 
size diagram for the usual American locomotive link-motion 
will require a sheet of paper 54 inches long and 27 inches wide; 
if two pieces are used, that at the crank-shaft may be 14 inches 
square and the other at the link may be 24 inches horizontally 
and 27 inches vertically; in either case the centre-line may be 
about 16 inches below the top of the paper where the link con- 
struction is to be made. 

Place the disk on the paper so that the hole at O shall come 
at the proper location for the centre of the crank-shaft, and 
drive a screw through that hole into the drawing-board; this 
gives the final location of the disk, and, like all the work for this 
use of the model, must be done carefully. Further instruc- 
tions direct the disk to be taken up and afterwards replaced, 
and in like manner certain other parts of the model are assem- 
bled and separated for testing and again put together. If this 
work is done carefully and with discretion, the model when fin- 
ished and ready for use will be free from back-lash and other 
sources of error and will endure much more use than required 
for working out any single problem. It is needless to say that 
haste or carelessness can easily ruin the model at any stage of 
the work. 

Have a strip of wood prepared to clamp to the disk, as shown 
by Fig. 2, PI. XXa, with two holes, one to receive the body 
of the ccrew at E and another to receive a pencil at Q. The 
latter will be placed at a distance from O equal to the radius 
of the crank-circle which, as already said, may be 6 inches. 
These holes are to be laid out and drilled with care according 
to the general directions. The path of the crank-pin can now 
be drawn with this device clamped to the disk and will be 
properly centred. 

Remove the disk and draw the centre-line corresponding to 



68 VALVE-GEARS FOR STEAM-ENGINES. 

XX', PL XX, through the centre of the hole for the screw which 
passed through O in the disk. Having the crank-pin circle 
already drawn, this may be done accurately by choosing one 
point at A and locating the other, A ', exactly opposite by spacing 
around the circle with dividers. The line XX' is to be pro- 
duced across the entire drawing by aid of a steel straight-edge, 
or a very fine thread drawn taut across the drawing. With the 
proper ratio of connecting-rod to crank, lay off the stroke xx r and 
locate the one-third stroke marks as indicated for both forward 
and return stroke. It will be convenient at the same time to 
locate the following divisions of the stroke, beginning at x, 
namely: \, \, f, f, and f, or, in place of the latter, the full- 
stroke cut-off as determined by Zeuner's diagram. 

To test the eccentricity, make a testing-piece of a strip of wood 
about 8 inches long, drilled to take the body of the screw at E' 
and a pencil at /, as shown by Fig. 3, PL XXa. Clamp the disk 
in place and turn it until the line OL through E' comes to the 
axis XX' and draw a short arc cutting that axis at J. Apply 
the testing-piece to the eccentric E and bring the line OK to the 
axis and again draw an arc across the axis; if the arcs coincide, 
the eccentricity is the same for both eccentrics; if not, the disk 
must be laid out and drilled anew. 

To test the angular advance, set the disk with the mark that 
represents the centre of the crank-pin on the axis XX', as indi- 
cated in Fig. 4, PL XXa, and with the testing-piece first on 
E and afterwards on E' describe arcs cutting the axis; if the 
intersections coincide, the eccentrics have the same angular ad- 
vance; if not, the disk may be turned by trial until a coincidence 
is secured and the centre-line AB representing the crank may 
be located midway between the eccentrics by marking the point 
on the disk which then comes on the axis. Of course, this method 
should be used only when the discrepancy is small; if it is 
large, the disk must be laid out again from the beginning. 

To lay out the link-template, draw an arc ZZ', Fig. 5, PL XXa, 



LINK-MOTION. 69 

with beam -compasses, using the proper radius for the link- arc 
and a convenient centre on the axis XX'. Place the template 
on the paper in contact with this arc and with its middle point 
on the axis XX'. Mark the points q and r on the edge of the 
template and square them up onto the face, then draw the line 
qr on the template. With the centre already used and with a 
radius equal to that of the link-arc minus the distance the link- 
pins are set back from the arc, draw the short arcs yy x and y 2 y% 
as shown. Draw two lines parallel to qr and at a distance from 
it equal to half the distance between the link-pins; this can be 
conveniently done by drawing arcs with the proper radius from 
a point near r and another near q. These lines PV and P'V 
will locate the centres P and P' of the link-pins. Produce 
these lines to the edge of the template and square down to the 
under surface. At P and P' small holes are to be drilled for the 
shanks of the screws. To test the accuracy of this construction 
place the template again in the position shown by Fig. 5 and 
weight it to prevent accidental movement, and then with the 
testing-piece attached first at P and afterwards at P', draw arcs 
intersecting the axis XX' on both sides, as shown. If these inter- 
sections coincide, the link-pins are accurately located ; if not, we 
must either relocate qr by trial or reconstruct the location for P 
and P' ; the latter procedure is to be preferred. 

Saddle-pin block. — While it is possible to locate the saddle- 
pin directly on the link-template, it is convenient to use an adjust- 
able block like that shown by Fig. 6, PI. XXa, which has two 
slots through which round-headed screws with steel washers may 
be passed to clamp it to the link -template. Draw a line pr 
across the face of the block and square down at the sides to 
the lower surface. At a point about one-fourth of an inch from 
the right-hand end locate a point m for the saddle-pin and drill 
a small hole for the shank of a screw. Place the block on the 
template with pr on the middle line qr of the template and with m 
about half an inch from the link-arc and locate holes for the 



L 



70 VALVE-GEARS FOR STEAM-ENGINES. 

round-headed clamping-screws so that the block can be moved 
back or forth half an inch. The holes for the clamping-screws 
are then to be drilled and the block clamped temporarily in place. 

Eccentric-rods, hanger and tumbler-arm. — One of the eccentric- 
rods is to be laid out with a length equal to the radius of the 
link-arc minus the distance the link-pins are set back from the 
arc, and then both rods are clamped together and drilled at 
both ends with large holes for the bodies of the screws. 

The hanger is to be laid out with the proper length and drilled 
with a large hole at each end. The tumbler-arm is also to be 
laid out with the proper length and drilled with a small hole 
at one end and a large hole at the other. 

First test o] the model. — Assemble the crank-disk, link-template 
and eccentric-rods, placing proper wooden washers under the back- 
ing rod, and place the model in its proper location on the drawing- 
board with a screw at O, Fig. 2, PL XX. To make a preliminary 
test of the model, place the crank-disk with the forward eccentric at 
its head-end dead-point and place the link-template so that the point 
V (Fig. 5, PI. XXa) comes on the axis XX', and mark that location 
by drawing a small portion of its arc near V across the axis with 
a sharp pencil. Set the same eccentric on the crank-end dead- 
point and repeat the operation. Make the same construction 
with the backing eccentric on the axis. If the arcs thus drawn 
with the two eccentrics on the head-end dead-point intersect, and 
those drawn with them on the crank-end dead-point also inter- 
sect, the link-model is satisfactorily laid out and assembled as 
far as we have gone. 

If this test fails, the trouble may be in one of three places: 
(1) the lengths of the eccentric-rods, (2) the location of the link- 
pins, or (3) on the crank-disk. The rods may be tested by inter- 
changing them; if they are found to be right, test the link-tem- 
plate by reversing it; if it also is right the error must be on the 
crank-disk, which must be tested again by the methods already 
given. In all the tests for accuracy, the methods given insure 



LINK-MOTION. 71 

symmetry rather than absolute correctness, namely, such tests 
show that the eccentrics have the same eccentricity and angular 
advance, that the eccentric- rods have equal lengths, and that the 
link-template is symmetrical with regard to its arc and the diam- 
eter at its middle point. These are exactly the properties that 
a link-motion must have in practice; slight variation from abso- 
lute dimensions have trifling effect on the valve-action. 

Full-gear Lead. — Having the model assembled and tested, it 
may now be used to ascertain what method of suspension will 
produce the desired valve-action and to determine completely the 
effects of that action. 

Set the model with the crank at a dead-point, with the crank 
on the axis XX r , Plate XX, and with the upper link-pin P on 
the same axis, and draw a short part of the link-arc across the 
axis with a sharp pencil. Place the crank on the other dead- 
point and repeat the operation; this will locate the points c and c\ 
the distance between which should be twice the lap plus twice the 
full-gear lead, as shown on Zeuner's diagram, Fig. 1, PI. XX, 
because the model thus shows twice the valve-dispiacement from 
mid-position when the engine is on a dead-point. If there is a 
slight discrepancy, it may be neglected ; a notable difference will 
demand a reconstruction of the model with stricter regard to 
actual dimensions as well as symmetry. 

In this construction it is important that the link-pin P shall 
be placed accurately on the axis XX'. One way is to stretch 
a fine line over the axis across the model and see that the centre 
of the screw at the point P comes under that line; the incon- 
venience of this method is due to the fact that the eccentric-rod 
may be so placed as to require a long line. Another way is 
to draw a perpendicular to XX' near the location of P and on 
it establish two points equidistant from that axis; with a pair 
of compasses the template may be placed equidistant from these 
reference-marks and consequently exactly on the axis. 

Having located c and c' , Fig. 2, PI. XX, the distance between 



72 VALVE-GEARS FOR STEAM-ENGINES. 

them may be bisected and from the middle point o the laps may 
be laid off on either side, these locating the point n and n'. These 
points are very important in the future work with the model 
and it is convenient to locate them by drawing a circle with the 
proper radius from o, as shown to a larger scale by Fig. 7, PL 
XXa; some draughtsmen draw that circle immediately in ink 
to make it distinct. Another circle may be drawn at the same 
time with a radius equal to the exhaust-lap. 

Location of Rocker. — The axis of the rocker may be located 
on a line oT perpendicular to XX', Fig. 2, PI. XX; to avoid 
disturbing the motion of the valve at cut-off and admission, T 
may be chosen so that an arc from T with a radius equal to the 
length of the rocker-arm shall pass through n and n' (see also 
Fig. 7, PL XXa). Since the arc through n and nf is short, nearly 
the same result will be obtained if oT is made directly equal to 
the length of the rocker-arm, but in such case n and n' will be 
slightly above the axis XX' . 

Location of the Saddle-pin. — As already pointed out the 
location of the saddle-pin is the most important single item in 
a link-motion design, and it is fortunately entirely under the 
control of the designer. A very good action of the valve will 
usually be obtained if the reverse-shaft is so located that its arm 
shall be horizontal when the link is in mid-gear, and if the 
saddle-pin be then located to equalize the cut-off at one-third stroke. 
For this purpose we may proceed as indicated on Plate XX, 
and more distinctly by Fig. 7, PL XXa. First, the model may 
be placed with the crank at R' corresponding to cut-off at one- 
third stroke, and the link-template may be moved till its arc 
comes to the point n', which corresponds to a valve-displace- 
ment equal to the steam-lap as should be the case at cut-off. Draw 
a bit of the link-arc and mark the ends of the line 0Y, and after 
the model is moved aside draw that line on the paper. Repeat 
the operation with the piston at one- third stroke at the other 
end of the cylinder and so locate the line qr. With the location 



LINK-MOTION. 73 

of the reverse-shaft already decided upon, the path of the saddle- 
pin while the template moves from q'r' to qr, will be very nearly 
horizontal. Consequently the saddle-pin m may be located on 
Fig. 7, PL XXa, by drawing by trial a horizontal line mm' which 
shall be so placed that mr shall be equal to m'r' . Having deter- 
mined this distance, mr or m'r', which the saddle-pin shall be 
placed back from the link-arc, the block shown by Fig. 6, PL XXa, 
may be properly located and clamped to the link-template. 

Location of the Reverse-shaft. — The centre of the reverse- 
shaft arm S, Fig. 2, PL XX, may now be located as follows: Bisect 
the line mm' (shown also on Fig. 7, PL XXa) by a line per- 
pendicular to the axis XX' and on it locate No at a distance 
from the axis equal to the length of the hanger; draw NoS parallel 
to the axis and make it equal to the length of the reverse- shaft 
arm. Drill a hole in the drawing-board at S and connect up the 
hanger with wooden washers at N and m' to give proper clear- 
ance so that the model may work freely. 

Final Test of Model.— Having the model connected, the crank 
should be set to give cut-off at one-third stroke at one end, as at 
R', Fig. 2, PL XX; the reverse-shaft arm is to be raised or lowered 
till the link-arc touches the corresponding lap-point n' '; place a 
weight on the reverse-shaft arm and turn the model till the link 
touches the other lap-point n; if the crank is now at the proper 
point R, corresponding to one-third stroke, the model is ready for 
service. If there is any discrepancy, it may be eliminated by 
shifting the saddle-pin m a slight distance. 

Alternate Location of Reverse-shaft. — If the ratio of crank to 
connecting-rod is unfavorable, it may appear in the investigation 
of the valve-action that the cut-off may be very unequal at and 
near full-gear. Sometimes a better action can be had by a 
different location of the reverse- shaft, by aid of which the cut-off 
may be equalized at another point of the stroke. 

Suppose that the work has proceeded as already described 
so far as the location of the saddle-pin, and that the reverse-shaft 



74 VALVE-GEARS FOR STEAM-ENGINES. 

is to be located so as to give equal cut-off also at two-thirds stroke. 
For this purpose let the model be set so that the crank comes at 
R a , corresponding to two-thirds stroke at one end, as indicated by 
Fig. 2, PL XXI, and let the template be moved so that the link- 
arc touches the lap-point w; again place the crank at Rb, corre- 
sponding to two -thirds stroke at the other end, and move the 
template till it touches the other lap-point n' ; the two positions 
m a and w& of the saddle-pin are to be located on the paper when 
the template is in the proper positions. Now take m a and m& as 
centres and with the length of the hanger as a radius draw arcs 
intersecting at N a . The entire operation may now be repeated 
in backing gear, but the construction thus made will be found 
to be symmetrical with that for forward gear, and the corre- 
sponding locations of the saddle-pin, m a r and m h ' ', will be sym- 
metrical with m a and m b and can be located above XX' directly 
without the trouble of a second construction. With m a f and m b r 
as centres and with the hanger as a radius, arcs are to be drawn 
intersecting at Nb. With N a and Nb as centres and the length 
of the arm N a S' as a radius, arcs are to be drawn intersecting 
at S f , the alternate location of the reverse-shaft. 

This location of the reverse-shaft is likely to disturb the 
equalization of cut-off at one- third stroke; this can be tested as 
described on page 70, and an adjustment can be made which 
in turn is liable to derange the cut-off at two-thirds stroke, but 
unless this latter effect is pronounced no attention need be paid 
to it. 

Comparing Plates XX and XXI, it is evident that S f , the 
alternate location of the reverse-shaft, is nearer XX f than is S, 
the original and simpler location ; not unf requently such a location 
will make it interfere with the eccentric-rods in backing gear. 

This alternate method lacks precision, since the points m a 
and mb, and also md and mrf, are too near together to give a 
satisfactory determination of the points N a and Nb', but in 
compensation, so long as the construction is symmetrical, a con- 



LINK-MOTION. 75 

siderable deviation of the shaft from S r will have comparatively- 
little effect on the valve- action. 

Lead, Port-opening and Slip. — After the locations of the 
saddle-pin and reverse-shaft are completed, the model is then 
to be used to test the action of the link in all grades, forward 
and backing. To do so, place the. reference-mark on the crank- 
disk, at the crank-position corresponding to a chosen piston- 
position (for example, at half-stroke forward); adjust the link- 
template so that its arc shall come to the point n, Fig. 2, PI. 
XX, and place a weight on the reverse-shaft arm. Turn the 
crank-disk and thus move the model till the link-template comes 
to the point n'\ note the position of the reference-mark on the 
crank-template, and find and record the corresponding position 
of the cross-head on its path xxf . 

With the same setting of the model find the lead, port-open- 
ing and slip. The first will be found by placing the crank on 
the dead-points. The second must be found by noting the 
greatest displacement of the link-arc from n toward the right, 
and from n' toward the left; these quantities are to be measured 
on a horizontal chord, not on the arc, since they represent the 
valve-displacements minus the lap. To find the slip, find and 
mark the highest point on the link-arc that comes to the arc 
through nti', and also the lowest point; the distance between 
these points is the slip of the link-block. 

This investigation of the action of the link should be car- 
ried on systematically for a sufficient number of points of the 
stroke, and recorded in a table similar to that on page 78. 

Should the action of the link-motion be deemed unsatisfac- 
tory, experiments may be made by changing the various dimen- 
sions of the link, so far as possible, following the general direc- 
tions on page 57. It is probable that the most troublesome 
element will be the slip of the link-block due to the attempt to 
equalize the cut-off, and with the method of suspension shown 
on Plates XIII and XX this is worse in forward than in backing 



76 VALVE-GEARS FOR STEAM-ENGINES. 

gear. When feasible, this unfortunate condition may be 
reversed by supporting the link from below, with which 
arrangement the slip in forward gear will be less than in 
backing gear. 

In this use of the model it will be found that the forward 
-eccentric- rod will strike the washer placed at e', Fig. 2, PL XX. 
Perhaps the required setting can be obtained by turning the 
model in the reverse direction, or the requisite freedom may be 
had by cutting a notch at v; or the rod may be reversed and 
another notch can be cut at w. 

It is clear that a similar model can be made for the Gooch 
link-motion or for other gears like those described in the follow- 
ing chapter. 

To Set a Link-motion. — If a link-motion is designed for equal 
lead, it is set by a method like the first method for setting a slide- 
valve with equal lead. Place the link at full-gear forward; with 
the proper angular advance as near as may be for each eccentric 
and with the engine on a dead-point give the valve the proper 
lead ; turn the engine onto the other dead-point, and if the valve 
does not then give the proper lead, change the length of the eccen- 
tric-rod by half the error or obtain the same result by changing 
the length of the valve-spindle, and shift the eccentric till the 
proper lead is obtained. Place the link at full-gear backing and 
set the valve again, changing the length of the eccentric-rod and 
the angular advance as may be necessary. Now place the link 
again at full-gear forward, and see if the setting has been is- 
turbed by the changes of the backing eccentric and eccentric-rod; 
if it has, the valve must be reset by the same method. Place 
the link again in full-gear backing, and make any correction 
needed; very commonly none will be required. When a link- 
motion is designed to give unequal leads (a common practice on 
marine-engines), the process differs only in that the lead at each 
end must be made the proper amount. 

The second method given on page 34 cannot be used in setting 



LINK-MOTION. 77 

a link-motion, since the maximum port-openings are not likely to 
be equal. 

A rocker for a link-motion is designed to avoid interference 
with lead and cut-off (Fig. 7, PI. XXo), and when the valve 
is set this condition should be considered. A horizontal link- 
motion like Fig. 1, PI. XIII, will have the rocker set to swing 
equally from a plumb-line through T, when the engine is at 
the dead-points. 

The eccentric-rods for the link-motions on Plates XIII and 
XIV are joined to the eccentric-straps by T-heads and bolts. 
The length of the rods may be adjusted by placing slips of metal 
called shims under the head — a method which may appear crude 
but is really convenient and effective. The bolt-holes through 
the shims can be slotted through to one side in order that a shim 
may be put in or withdrawn without taking out the bolts. 

Application of Skeleton Model. — To illustrate the method, 
and to show the influence of changing some of the parts of a 
link-motion, there are given here the results of the application 
of the skeleton model to a few examples. 

The following dimensions were used in all the examples: 

Eccentricity 3 inches 

Steam-lap f inch 

Radius of link-arc 48 inches 

Length of hanger 16 ' ' 

Length of reverse-arm. . . '. 20 " 

Length of rocker- arm (when used) 12 ' ' 

Stroke 24 ' ' 

Ratio of crank to connecting-rod. 1:5 

In all the examples except that shown by Table II the dis- 
tance from the centre of the eccentric to the link-arc was equal 
to the radius of the link-arc; the length of the eccentric-rods 
from the centre of the eccentric to the link-pins was made less 
or more than this distance according as the link-pins were back 



73 



VALVE-GEARS FOR STEAM-ENGINES. 



of or ahead of the link-arc, except for the example shown by 
Table V, which had the link-pins on the link-arc. The saddle- 
pin in all cases is at the middle of the length of the link. Other 
dimensions of the link-motion and details of the arrangement 
are given with the tables. 

In the example shown by Table I the reverse- shaft was set 
square, i.e., with the arm horizontal at mid-gear as shown on PL 
XX, and the cut-off was equalized at ^ stroke only. This may be 
considered to be the typical example. The lead at full-gear, or 
with the cut-off at 22^ inches, is small, but increases rapidly as the 
cut-off is shortened, till it is nearly half an inch when the cut-off is 
at quarter stroke; meanwhile the travel and port-opening both 
decrease rapidly. The travel of the valve in full-gear is more 
than twice the eccentricity, due to the slip of the link-block and 
to other irregularities. 

TABLE I. 

Rocker used — link -pins 2J inches back of link-arc. 
Cut-off equalized at ^d stroke. 
Saddle-pin ^ of an inch back of link -arc. 
Distance between link-pins 14 inches. 



Cut-off. 


Lead. 


Slip. 


Travel. 


Port- 
ing. 


H°E. 


6 
CE. 


Diff. 
a&b. 


6 

9 
12 

15 
18 
21 
22-^ 


146 
I7l 

20f 
22 


I 

f 
f 
i 


t 


1 

\ 

1 


2§f 

3rs 

4§5 
6& 


f 
1 



An inequality in the cut-off of \ of an inch in 24 inches, i.e., 
one per cent of the stroke, cannot be distinguished in the running 
of the engine or on the indicator-diagram; consequently the 



LINK-MOTION. 



79 



cut-off may be considered to be equalized from \ to f of the 
stroke. The inequality of the cut-off becomes as large as § of 
an inch at 18 and 21 inches; but while such an inequality may 
possibly be distinguished on an indicator-diagram, it cannot 
have an appreciable effect on the running of the engine. 

In all the examples the gear was made symmetrical; conse- 
quently the action in backing gear was almost identical with 
that in forward gear, and need not be stated separately. 



TABLE II. 

Rocker used — link -pins z\ inches back of link-arc. 
Cut-off equalized at Jd stroke. 
Saddle-pin ^ of an inch back of link-arc. 
Distance between link-pins 14 inches. 



Cut-off. 


Lead. 


Slip. 


Travel. 


Port- 
ing. 


H.E. 


b 

C.E. 


Diff. 
a&b. 


6 

9 
12 

15 
18 
21 

22^ 


5ff 

8§f 
iif 
I4§§ 
I?! 

22 A 


1 

1 

A 
t 
1 


t 
1 

H.E. $• 
CE.A 


1 

4 

1 

§ 


2& 

2 ii 

3* 
4** 

6A 


IS 

f 

1* 

2 M 



In this example the eccentric-rods were made one inch longer 
than in the preceding example, which made the radius of the link- 
arc one inch shorter than required for the normal condition, 
i.e., 48 instead of 49 inches. The effect was to reduce the in- 
equality of the cut-off at long cut-off, so that the cut-off may 
be considered to be practically equal for the entire stroke. The 
full-gear lead had an inequality of t$ of an inch, but at other 
grades of the link the lead was sensibly equal. Had the link been 
set to give equal lead at full-gear, then the mid-gear lead would 
have had an inequality of & of an inch in half an inch, which 



So 



VALVE-GEARS FOR STEAM-ENGINES. 



would not have any appreciable effect in the running of the 
engine. 

In the third example the cut-off was equalized at \ stroke 
and at full-gear as recommended by Auchincloss in his Link 
and Valve-motions, by the method described on page 73 and 
shown on PL XXI. With the ratio of crank to connecting-rod 
used in these examples, i.e. 1 : 5, the reverse-shaft was found 
to interfere with the eccentric-rods at full-gear backing. The 
table shows that the equalization of the cut-off was nearly per- 
fect from half-gear to full-gear. The inequality in the cut-off 
increases as the cut-off is shortened, that is, at the place where 
it has the most deleterious effect ; but it must be admitted that 
an inequality of f of an inch in 6 inches cannot have a very bad 
effect, if indeed it should be distinguishable in the running of 
the engine. Both the danger of interference of the reverse-shaft 
with the eccentric-rods and the inequality of cut-off near mid- 
gear will be found to be less with a more favorable ratio of crank 
to connecting-rod, or with the cut-off equalized at \ and § stroke 
as recommended on page 73 and shown on PI. XXI. 



TABLE III. 

Rocker used — link-pins 2J inches back of link-arc. 
Cut-off equalized at \ stroke and at full-gear. 
Saddle-pins ^ of an inch back of link-arc. 
Distance between link-pins 14 inches. 





Cut-off. 










Port- 










Slip. 


Travel. 






b 


Diff. 










H.E. 


CE. 


a&b. 










6 


i 


ft 


T^ 


& 


2M 


A 


9 


A 


A 


A 


2\ 


\ 


12 


12 





*} 


44 


2\ 


f 


15 


I4§2" 


A 


t 


h 


3t* 


If 


18 


i7# 


A 


A 


to 


3f 


iA 


21 


20M 


A 


A 


1 


4tt 


if 


22§ 


«tt 


A 


H.E. O 


il 


6\ 


2\ 



LINK-MOTION. 



81 



The fourth example had the reverse-shaft set square and 
differed from the first example in that the link was made shorter, 
i.e., 12 instead of 14 inches between the link-pins; the link-pins 
were also set back 3 inches instead of 2|, but such a change 
has not much effect. A comparison of this table with Table I 
will show that shortening the link increases the irregularities of 
the link-motion, and especially that it increases the slip at all 
gears. 

TABLE IV. 

Rocker used — link-pins 3 inches back of link-arc. 
Cut-off equalized at \d stroke. 
Saddle-pin §§ of an inch back of link-arc. 
Distance between link-pins 14 inches. 



Cut-off. 








Port- 


















b 


Diff. 








ing. 


H.E. 


CE. 


a&b. 










6 


5l 


i 


1 


f 


2& 


If 


9 


8# 


TS 


1 


ft 


2M 


M 


12 


"tt 


T5 


■A 


1 


2« 


A 


iS 


I4f 


f 


A 


M 


att 


f 


18 


i.7§ 


f 


A 


if 


3i 


1 


21 


20| 


f 


*j 


II 


4i* 


if 


22^ 


22 


1 


H.E. ^ 
CE. & 


If 


6A 


*A 



Example five was chosen to represent the type of link-motion 
which acts directly on the valve-spindle without the intervention 
of a rocker, and, as is customary, has the link-pins on the link- 
arc. It may be compared with Table IV, which has the link- 
pins the same distance apart. The equalization of cut-off from 
\ to f stroke is good, though not perfect, and the inequality at 
and near full-gear cannot have a very bad effect, though it is 
much larger than in the fourth example. The slip is less than 
for that example at all grades; but probably the slip could be 
much reduced in such a link-motion with a rocker, if the link- 



32 VALVE-GEARS FOR STEAM-ENGINES. 

pins were placed nearer the link-arc or on the link-arc. Such 
an arrangement would show greater inequality in cut-off than 
is found in Table IV. 

TABLE V. 
Link acts directly on valve-spindle without rocker. 
Link-pins on link -arc. 
Cut-off equalized at Jd stroke. 
Saddle-pin \ of an inch forward of link-arc. 
Distance between link-pins, 12 inches. 



Cut-off. 


uL 


Slip. 


Travel. 


Port- 
ing. 


H.E. 


b 

CE. 


Diff. 

a&b. 


6 

9 
12 

15 


6| 
9tV 

III 

i4f 


I 

1 

f 


i 
f 
I 


fir 

■h 

1 


2T6 

a 

2f 


if 

1 

ft 


18 


17* 


S 


^i 


1 


3i 


H.E. I 
CE. 1 


21 


20& 


11 


A 


} 


4i 


H.E. if 
CE. l\ 


22^ 


21J 


f 


A 


1 


6^ 


H.E. 2f 
CE. 2^ 



The sixth example was chosen to show the effect of placing 
the link-pins ahead of the link-arc, on a link which acted directly 
on the valve-spindle without the intervention of a rocker. Such 
an arrangement would require the use of a side-bar link or a 
box-link (shown by Fig. i, PL XIV, and Fig. 3, PL XVIII), 
and might involve some mechanical difficulties. 

The equalization of the cut-off must be considered to be 
satisfactory, but it is attained at the expense of an excessive 
slip of the link-block. Probably a compromise between the 
link-motions shown by Tables V and VI, having the link-pins 
an inch or an inch and a half ahead of the link-arc, would be 
found to give a fair equalization of the cut-off without excessive 
slip. Also greater distance between the link-pins (14 instead 
of 12 inches) could be used with advantage. 



LINK-MOTION. 

TABLE VI. 

Link acts directly on valve-spindle without rocker. 

Link -pins 3 inches ahead of link -arc. 

Cut-off equalized at ^d stroke. 

Saddle-pin if of an inch ahead of link-arc. 

Distance between link-pins, 12 inches. 



83 



Cut-off. 


„, 


Slip. 


Travel. 


Port- 
ing. 


H.E. 


b 

C.E. 


Diff. 
a&b. 


6 

9 
12 

15 
18 
21 

22§ 


6| 

nil 

I4f 

i7tt 

22f 


t 

i 


1 
1 

A 
i 

4 


iff 
itt 
ift 
ift 

if 
if 
if 


2^ 

at 
af 

ail 

3i 

4! 

6J 


f 
ft 

1 

2& 



CHAPTER IV. 
RADIAL VALVE-GEARS. 

The name radial valve-gear has been applied to a number 
of reversing-gears that differ widely in detail and in general 
appearance, but agree in that they derive the mid-gear motion of 
the valve from some source that is equivalent to an eccentric 
with 90 angular advance, and they combine with this motion 
another that is equivalent to that of an eccentric with no angu- 
lar advance. The general conception of this form of valve- 
gear is most easily obtained from an example. 

Wals.chaert Gear. — This gear is chosen as the first example 
of the type because the elements are easily distinguished. In 
Fig. 1, PI. XXII, H is the engine cross-head, and a is the head 
of the valve-spindle. The valve is moved through a radius- 
rod, one end of which carries a block that may be set at any 
position in a slotted link dF, and the other end takes hold of a 
combining-lever af, that receives motion from the engine cross-head. 
The slotted link swings on a fixed trunnion at G and is moved 
by an eccentric OE, which has no angular advance. In Fig. 2 
the diagram in thin lines shows the gear at a dead-point, and 
the diagram in heavy lines shows the gear when the crank has 
moved through the angle C O =0. 

If the motion of the engine cross-head can be considered to be 
harmonic, then it is clear that the motion that it gives to the valve 
could be derived from an eccentric with 90 angular advance; this 
motion is made equal to twice the lap plus twice the lead. If the 

84 



RADIAL VALVE-GEARS. 85 

block d is at the middle of the link, the valve will derive motion 
from the cross-head only and the mechanism will be at mid-gear. 
The radius of the link-arc is made equal to the length de of the 
radius-rod, consequently the lead is constant for all settings 
of the gear. If the point h of the guiding-link hj were a fixed 
point, then the valve would receive motion from the eccentric OE } 
which has no angular advance. By placing the link-block nearer 
the trunnion G the motion is reduced; for example, the motion 
communicated from the eccentric OE will be half as much if the 
block is half-way between d and G. If the link-block is below 
G, the motion is eversed 

It is shown in the appendix, that the motion imparted to a 
valve by this gear can be approximately represented by Zeuner's 
valve-diagrams like those used for a shifting-eccentric. As usually 
constructed, this gear does not give harmonic motion to the valve, 
for the motion of the cross-head of the engine with the usual pro- 
portions of locomotives has considerable irregularity on account 
of the angularity of the connecting-rod; also some irregularity 
is introduced by the combining-lever a}. Consequently such a 
diagram as Fig. 1, PL XXI, can be of use only in roughly block- 
ing out a gear. The real action of the gear can be determined 
either by constructing diagrams similar to Fig. 2 on as large a 
scale as convenient, or by aid of a model. A combination of 
the two methods, similar to the skeleton model for link-motions, 
may be found convenient for this purpose. Since part of the 
motion of the valve is derived from the cross-head, the adjust- 
ment of the gear to give equal cut-off will generally be easier than 
for a link-motion. 

In laying out a Walschaert gear, the combination-lever af 
should be made vertical when the cross-head is at the middle of 
its stroke; the guiding-link hj should be made to vibrate equal 
angles above and below a horizontal line; a line from G to F on 
the link should be made vertical when the engine is on a dead- 
point; and the supporting-link with the reverse-arm ST should 



86 VALVE-GEARS FOR STEAM-ENGINES. 

be so laid out that c may be guided nearly on a horizontal line, 
unless the adjustment may be found to require a different arrange- 
ment. The length of the combining-lever should be so chosen 
that its angular vibration shall not exceed 6o°. 

The main dimensions of the gear for any engine will be im- 
posed on the designer by the general proportions of the engine 
and its frame. There are, however, two elements over which 
the designer will have more or less control: they are the position 
of the axis of the trunnion G, which in the figures is on the link- 
arc, but which may be placed either forward of or back of the 
link-arc; and the reverse-shaft T, which may often be located at 
will, within limits. The first will be found to have the most 
influence on the action of the gear. 

The eccentric OE is sometimes replaced by a return-crank 
from the engine-crank C. The link is sometimes turned the 
other way, in which case the radius-rod extends forward from 
the head of the valve-rod. 

Marshall Valve-gear. — Plate XXIII shows the Marshall valve- 
gear as applied to the U. S. S. Yorktown. In Fig. i, XX' is the 
axis of the cylinder, O is the centre of the shaft, and C is the 
crank-pin. The eccentric centred at E gives motion to a short 
and massive eccentric-rod EG, which is guided at o by the link 
oD, and is connected to the valve-spindle V by a valve-rod GV. 
The guiding-link oD is supported~by the bell-crank lever DoS, 
having its axis at o; the rod ST gives connection with the reverse- 
shaft arm TV. In the figure the engine is at a dead-point, so 
that the guided point of the eccentric-rod coincides in projection 
with the axis of the bell-crank lever. 

Fig. 2 shows the centre-lines of the gear in two positions ; the 
heavy lines are for the full-gear of the valve-motion, and the fine 
lines are for a gear between that and the mid-gear. OC is the 
centre-line of the crank; E is the centre of the eccentric; FD is 
the guiding-link; and oD is the arm of the bell-crank lever, hav- 
ing its axis at o. 



RADIAL VALVE-GEARS. 67 

When the bell-crank lever is set to give the mid-gear action 
of the valve, D is found at Do, and the guided point F moves 
on an arc of a circle that nearly coincides with the line OF; the 
point E describes a circle, and all other points of the eccentric- 
rod except F describe ovals that are more or less elongated as they 
are near or removed from the guided point F. In this setting of 
the gear the horizontal motion of the point G is made equal to twice 
the lap plus twice the lead, so that the valve receives a motion like 
that given by an eccentric having 90 angular advance ; as G is 
beyond F, the eccentric E properly coincides with the crank. 

At any other gear than mid-gear, for example with D set for 
full-gear, the vertical displacement of F will have two compo- 
nents, one along the axis. OY, and one perpendicular to it. The 
second component with some modification is transferred to G 
and gives to the valve an additional displacement like that from 
an eccentric with no angular advance. This gear is consequently 
of the general type described at the beginning of the chapter, but 
the various irregularities of the gear are so marked that the valve- 
diagrams similar to Fig. 1, PL XXI, cannot be used at all in de- 
signing and laying out the gear. Since the guided point F is 
always brought into coincidence with the axis of the bell-crank 
lever when the engine is on a dead-point, the lead is the same 
for all gears. 

The cut-off is shortened by making D approach D ; the 
thin lines show the gear set for a cut-off at about f stroke. The 
engine is reversed by carrying D beyond D toward D" . 

Fig. 3 gives the valve- ellipses for full- gear and for a short 
cut-off, corresponding with the diagrams in full lines and finer 
lines shown by Fig. 2. The valve- ellipses show the defect of 
the gear, which is a marked inequality in the maximum port- 
opening. This defect may be overcome by an adaptation of 
Prof. Sweet's method (page 25) for equalizing the cut-off of a 
plain slide-valve with the aid of a rocker or bell-crank lever. 

In some cases the point G is taken between the eccentric 



o8 VALVE-GEARS FOR STEAM-ENGINES. 

and the guided point, in which case the eccentric is set opposite 
the crank. 

The design of the Marshall valve-gear must be carried 
out by the aid of diagrams or a model, or by a combina- 
tion of the two methods, which appears to be well adapted for 
this work. 

Hackworth Valve-gear. — This gear differs from the Mar- 
shall gear in having the guided point carried by a block that 
slides in straight guides and thus avoids the irregularity due 
to the guiding-link. The irregularity of the valve-motion is less 
than when the Marshall gear is used, and the maximum port- 
openings can be made nearly equal. The pressure on the sliding- 
block is large, especially at full-gear, and unless ample wearing 
surface is provided the friction and wear are liable to be ex- 
cessive. In some cases the sliding-block has been provided with 
rollers to reduce the friction. 

Joy Valve-gear. — An example of the Joy valve-gear used 
on the Pennsylvania Railroad Company's tugboat Delaware is 
shown by PI. XXIV. XX' is the centre-line of the crank and 
connecting-rod, xx f is the centre-line of the valve-spindle. The 
lever abc is guided at one end on a flat arc by the rod 
gc, and at the other end is attached to the connecting-rod 
at the point a, which describes an oval having the length 
a& 2 equal to the stroke of the engine. This oval, which 
is omitted to avoid confusion of the diagram, is symmetrical 
with regard to the axis XX', and is slightly more pointed 
at the cross-head end than at the crank end. The point b, 
which describes the irregular oval bbib 2 , takes the place of the 
centre of the single eccentric used with the Marshall valve-gear 
(PI. XXIII), and acts on the lever Me. The point i of the lever 
Me is guided on the circular arc //i by the sliding-block B, and 
the point e, which describes the oval eeie 2 , carries the valve- 
rod ed. The connecting-rod CD, the valve-rod ed, and the rod 
eg are in one plane; the levers ac and be and the curved guide- 



RADIAL VALVE-GEARS. 89 

bar //1 are double, one system being on each side of the connecting- 
rod ; in the figure the system of levers in front of the connecting- 
rod is omitted to show the construction more clearly. The 
guided point i could evidently be guided on the arc ff 1 by a link 
centred at k; such a construction is frequently used in marine 
engines. A comparison of this gear with the Marshall valve- 
gear will show much similarity. The essential points of differ- 
ence are : (1) the radius of the guiding-arc //1 is always equal 
to the length of the valve-rod, and (2) the irregularity due to the 
angularity of the lever bie is compensated by the action of the 
lever ac, somewhat in the manner that the linkage known as Watt's 
parallel motion is made to give nearly a straight-line motion. 
These advantages are attained at the expense of greater com- 
plication and cumbersomeness. It may be remarked that 
the inequality of port-opening, which is the notable defect 
of the Marshall gear, may be nearly if not quite remedied by 
making the length of the guiding-link equal to the valve-rod, 
but such a construction is usually impracticable, since it requires 
either an impossible length for the guiding-link, or else a short 
valve-rod and a long valve-spindle that must be guided at the 
outer end. The guiding-bars // t are hung on trunnions with 
the axis at the point i 1} and are connected at / to the reversing- 
lever. The gear is shown at full-gear for left-handed rotation; 
It may give a shorter cut-off if the guiding-bars //1 are given less 
inclination from the horizontal or mid-gear position, and when 
in mid-gear it will give the valve a motion equal to twice the lap 
plus twice the lead; if the guiding-bars //1 are inclined the 
other way, the engine will be reversed. 

This gear, when properly proportioned, gives a rapid motion 
to the valve when opening and closing, less compression at short 
cut-off than does a link-motion, and the cut-off can be made 
nearly equal for all grades of the gear. Like all other radial 
valve-gears, it gives a constant lead. Its defects are the number 
of parts and of joints that are liable to wear loose, and the 






90 VALVE-GEARS FOR STEAM-ENGINES. 

obstruction that it offers to inspection and care of the crank-pin 
and cross-head when the engine is run. 

To lay out a Joy valve-gear: Choose a point a on the con- 
necting-rod, having a transverse throw equal to twice the maxi- 
mum displacement of the valve; make the length of the lever ac 
such that the angle a\C\a 2 shall not be more than 90 ; draw 
the centre-line xx' of the valve-stem, and locate the point eo 
opposite the middle-point of the line a 1 a 2 ; lay off e$ex = e§e 2 
equal to the lap plus the lead; lay off aib 1 = a 2 b 2 equal to about one 
third of fliCi; and draw the lines eih and e 2 b 2 intersecting at ii; 
this last point locates the axis of the trunnions carrying the guiding- 
bars }}i. If the point i is guided by a link, then the arm carrying 
the link must be centred at i\ ; in the figure the position of such 
an arm is shown by the line i\k. Finally, the valve- ellipse should 
be drawn for several grades of the gear; in the figure the valve- 
ellipse oo\ has its length equal to the stroke of the engine, and 
the valve-displacements are magnified fourfold, i.e., st = ^dod. 
Usually the axis xxi of the valve-motion is determined by the 
general design, and cannot be changed much, if at all. The 
length of the lever ac will commonly be as great as desirable 
if the angle a x cia 2 is something less than 90 ; it cannot be made 
shorter without throwing excessive stress on the links and levers. 
The transverse motion of the point a is properly twice the maxi- 
mum displacement of the valve, in order that the inclination 
of the g.uide-bars //1 may not be more than 25 or 30 ; should 
such a location bring the lever ac too near the shaft, as may be 
the case when the crank is counterweighted, then a may be placed 
nearer the cross-head, but at the expense of more inclination of the 
guiding-bars at long cut-off. The location of the point b is under 
the control of the designer, and may be used to equalize the cut-off 
either at that grade at which the engine is to run habitually, 
or else to give nearly equal cut-off at all grades. The equaliza- 
tion of the cut-off must be made by trial, and no general rule 
can be given, since the elements, such as the length of the lever 



RADIAL VALVE-GEARS. 91 

ac and the distance between the axes xx' and XX', over which 
the designer has little control, have a large influence. A skeleton 
model may be used to advantage in this work. It should have 
rods to represent the connecting-rod, the levers ac and be, and 
the links eg and ki. The point k will be located on an arc of a 
circle centred at i\. The points i and b on the levers be and ac 
should be made adjustable; the first by mounting it on a sliding- 
block that can be clamped in any desired position, and the second 
by that method, or by a series of holes to receive the screw repre- 
senting the pin at b. It may be found advantageous to provide 
pieces, properly guided, to represent the cross-head and head of 
the valve- spindle, but a simple model may be made by placing 
these points by hand on the lines XX' and xx' for the several 
positions of the model, and the centre C may in like manner be 
placed on the circle CC"C. 



CHAPTER V. 
DOUBLE VALVE-GEARS. 

A plain slide-valve, set to give an early cut-off, is liable to 
give either an excessive compression or an early release, or both. 
A single valve under the control of a gear that gives a variable 
cut-off, such as a shifting- eccentric or a link-motion, is open to 
the same difficulties; and in addition the compression varies 
with the cut-off, though to a less degree. For a stationary engine 
a large compression may be undesirable, and a varying compres- 
sion is always so. To avoid these difficulties two valves are 
frequently used: one, called the main valve, has an unvariable 
motion, and gives the admission, release, and compression; 
the other, called the cut-off valve, gives the cut-off only, which 
may be varied without affecting the other events of the stroke. 

The cut-off valve may be placed in a separate valve-chest, 
as shown by Fig. 3, PL XXV, or it may be placed on the back 
of the main valve, as shown by Fig. 1, PI. XXVI; thus giving 
rise to two separate types of double valve-gears. It is impor- 
tant to obtain a clear conception of the principles of double 
valves, and then all existing forms of double valve-gears may 
be readily understood, and a gear for a given purpose may be 
easily designed, or else it may be shown that a satisfactory design 
is impossible. 

Cut-off Valve in a Separate Valve-chest. — The usual arrange- 
ment of this valve-gear is shown by Fig. 3, PL XXV. The main 
valve, which receives motion from an eccentric with constant 
J 92 



DOUBLE VALVE-GEARS. 93 

angular advance and eccentricity, is designed to give the desired 
release and compression, and is set to give equal lead; it will 
be observed that either the release or the compression may be 
equalized. In the figure there is no exhaust-lap; this arrange- 
ment may be frequently found desirable, but it is chosen here' 
for the sake of simplicity, and will be adhered to throughout 
the chapter; attention will be given exclusively to the cut-off,, 
since the other features of the gear are the same as for a 
plain slide-valve and have received sufficient attention in the first 
chapter. 

In the figure the valves are shown disconnected from the 
eccentrics and both in mid-position; they cannot both be in 
such position when the gear is connected up, but such a draw- 
ing is convenient in laying out the valves. The cut-off valve is; 
a rectangular open frame having the acting edges inside. The 
distance / from one edge of the valve to the opposite edge of 
the port is the clearance of the valve; when the valve is dis- 
placed from mid-position an amount equal to the clearance, 
the cut-off valve gives either cut-off or readmission. The right- 
hand edge gives cut-off for the head end of the engine, and re- 
admission for the crank end; it is important that the readmis- 
sion by the cut-off valve should precede the admission by the 
main valve, in order that the second steam-chest shall then be 
properly filled with steam at full pressure. 

The steam-port a is for the passage of full-pressure steam 
only, and may consequently be made from \ to § of the area 
of the port a, through which exhaust-steam also must pass. Two 
or more ports are frequently provided in the cut-off valve-seat, 
and the valve is then known as a gridiron valve; in such case 
the combined area of all the ports a Q should be a little in excess 
of what would be given to one port, to allow for the greater fric- 
tion in numerous narrow passages. A gridiron valve acting 
on several narrow ports will require a proportionately less throw. 

In Fig. i, PI. XXV, OP is the diameter of the valve-circle 



94 VALVE-GEARS FOR STEAM-ENGINES. 

for the main valve which gives admission at ORq and ORd, and 
cut-off at OR. The eccentric acting on the cut-off valve is given 
a negative angular advance, i.e., it is less than 90 in advance of 
the crank; consequently the displacements of the cut-off valve 
from mid-position are given by a valve -circle, such as OPo, hav- 
ing its diameter laid off at an angle £0 (the negative angular 
advance) away from the crank. If the clearance is equal to 
Ol 2 , then the cut-off by the cut-off valve occurs at OR 2 and the 
readmission at OR. 

A variable cut-off by aid of this gear may be obtained by 
varying the clearance of the valve, or the throw of the eccentric, 
or by using a shifting-eccentric. Now, the same effect is pro- 
duced by increasing the lap (or decreasing the clearance) with 
a constant eccentricity as is produced by decreasing the eccen- 
. tricity with a constant lap; consequently an investigation of one 
of the two methods will serve for both. It will appear that 
neither will give a good variable cut-off. On the other hand, 
.a satisfactory gear may be had by using a shifting-eccentric. 

In Fig. 1, PL XXV, the clearance Ol 2 gives cut-off at OR 2 
and readmission at OR, coincident with the cut-off by the main 
valve: and OR 2 is the latest admissible cut-off; for if the clear- 
ance is made greater or equal to Oh in order to obtain a later 
cut-off at ORl, the readmission will occur at ORi , before the 
main- valve cut-off, and a double admission of steam will occur. 
Such a double admission causes a large waste of steam and an 
irregular action of the engine and cannot be tolerated. 

The earliest admissible cut-off is obtained by a clearance equal 
to O/3, which gives cut-off at OR 3 and readmission at ORd.. An 
inspection of the figure shows that the angle R 2 OR 3 must, from 
symmetry, be equal to RORd; the latter angle depends on the 
lap of the main valve, and it is at once evident that only a 
limited range of cut-off can be obtained with such an arrangement. 

In practice a gridiron cut-off valve was commonly used and 
the cut-off was obtained by varying the travel of the valve. For 



DOUBLE VALVE-GEARS. 95 

this purpose a fixed eccentric was connected to the end of a 
slotted lever or link, and motion was communicated to the valve 
from a link-block that could be set at any desired place in the 
link. To shorten 'the cut-off, the link-block was moved toward 
the fixed end or fulcrum of the link. An idea of this arrangement 
may be obtained by supposing the radius-rod of the Walschaert 
gear (Plate XXII) to act on the cut-off valve-spindle; the eccentric 
should, of course, have a negative angular advance, and only 
half of the link will be required. The effect of such an arrangement 
is the same as though the eccentricity were varied, and, just as 
has been shown to be the case for a gear with varying lap, the range 
of variation of cut-off depends on the lap of the main valve. 

Cut-off Valve with Shifting-eccentric. — If the cut-off valve 
in a separate valve-chest is moved by a properly designed shifting- 
\^eccentric, the readmission may be kept within the proper limits, 
4p i.e. before the admission for one end of the cylinder and after 
the cut-off for the opposite end by the main valve, and at the 
same time any desired range of cut-off may be had. 

In Fig. 2, PL XXV, let OP be the main valve-circle, giving 
cut-off at OR and admission at ORq. Suppose that the cut-off 
is to vary from ORi, corresponding with \ stroke, to OR co- 
incident with the cut-off by the main valve. Bisect the angle 
RORq by the line OPq, and bisect the angle RORi by the line 
OPo) then a valve-circle centred at CV can be made to give 
a cut-off coincident with that by the main valve, and readmission 
coincident with the main- valve admission; while a valve-circle 
centred at Co can give cut-off at OR\, and readmission coincident 
with the main-valve cut-off at OR. 

It is convenient to have the shifting-eccentric on an arm 
centred on the centre-line of the crank, or rather on that line 
produced, for then the cut-off gear will work equally well in 
forward and in backing gear on a reversing-engine ; but for a 
statiouary engine such an arrangement is not essential. We 
now have three elements of which one may be chosen at pleasure 



96 VALVE-GEARS FOR STEAM-ENGINES. 

and the other two will then be determinate. In the figure the 
diameter OP of the valve-circle to give early cut-off is made i^ 
inches, equal to the eccentricity for the main eccentric ; the clear- 
ance 01 of the cut-off valve is then determined by the intersection 
of that circle by the lines OR and OR u and is if of an inch. 
The centre Cq of the valve-circle to give the cut-off coincident 
with that of the main valve must be so chosen that it shall pass 
through O and l"\ it is on a perpendicular to 01" at its middle 
point. Draw AS perpendicular to the middle point of an imagi- 
nary line joining Po and Po'; then S, the intersection of this line 
with the axis XX', is the centre o an arc on which the point P 
will travel as the cut-off is shortened. The shifting-eccentric 
must be swung from a point on the centre-line of the crank produced 
and at a distance from the centre of the shaft equal to OS (if 
of an inch); when the crank is at OX this point will be at T. 
With ordinary proportions for an engine, the point T is liable to 
fall inside the shaft, or else so ear that the contruction of an 
arm for the eccentric will be impossible. A reversing-engine 
may have the following arrangement: fast to the shaft may be 
an eccentric with an eccentricity equal to OS and with its centre 
opposite the crank-pin; this eccentric may carry another having 
an eccentricity equal to AS (i|i of an inch); the second or outside 
eccentric will be turned toward the crank so that its angular 
advance will be negative. A stationary engine that always 
runs in one direction may have the swinging arm, for the eccen- 
tric controlling the cut-off valve, centred at any convenient point 
on the line AS produced. 

There now remains the determination of the width of the 
cut-off valve to prevent leakage past the outside edge. The 
greatest displacement of the valve from mid-position is equal to 
OPo = i| of an inch; consequently the distance in Fig. 3, PI. 
XXV, from the outside edge of the valve to the nearest edge 
of the port should be somewhat greater than 1 \ of an inch; it 
is made 1 A of an inch. 






DOUBLE VALVE-GEARS. 97 

The arrangement shown by Fig. 3, PL XXV, has an excessively 
large steam-chest for the main valve, which gives an undesirable 
action because the steam in that chest can flow into the cylinder 
with a decreasing pressure until the cut-off by the main valve 
occurs; it is commonly said that the steam in that chest takes 
part in the expansion. This defect can be ameliorated by reducing 
the height of the main valve and the size of its chest as far as 
possible; or a piston-valve taking steam in the middle can be 
used, or some other device may be invented to decrease the space 
thus affected. 

Cut-off Valve on back of Main Valve— Fig. i, PL XXVI, 
shows a cut-off valve on the back of the main valve, both being 
■ <Y disconnected from their eccentrics and placed in mid-position. 
When the gear is connected up, such a position of both valves 
at the same time does not occur, but it is convenient to make 
a drawing of the valves in that position to show the laps and 
other dimensions of the main valve, and the clearance and length 
of the cut-off valve. The main valve is designed to give the 
desired compression and release, and is set to give equal lead; 
either the compression or the release may be equalized. The 
cut-off valve is connected to an eccentric having a large angular 
advance, so that it is nearly (sometimes exactly) opposite the crank. 

In Fig. 3, OP is the diameter of the main valve-circle, and 
OPq is the diameter of a valve-circle showing the absolute dis- 
placements of the cut-off valve. At any crank-position, such 
as OR, the chord Oc intercepted by the main valve-circle shows 
the displacement of the main valve; represented in Fig. 2 by 
e. The absolute displacement of the cut-off valve is shown by 
the chord Ob, intercepted by the cut-off valve-circle; repre- 
sented by e in Fig. 2. Both of these displacements are toward 
the left, but the former being the greater, the relative displace- 
ment e x of the cut-off valve with regard to the main valve, and 
measured from the centre of the main valve, is towards the right, 
tending to shut the port in the main valve. 



9° VALVE-GEARS FOR STEAM-ENGINES. 

The displacement of the cut-off valve, or plate, to the right 
from the middle of the main valve can be represented by an 
auxiliary valve-circle having its diameter at OP x on Fig. 3, 
and which can be constructed by drawing OP x parallel and equal 
in length to the line PPq, which connects the points P and P . 
At the crank-position OR, the absolute displacements of the 
main valve and the plate, both to the left, are Oc and Ob, and 
the relative displacement of the plate from the middle of the 
main valve, toward the right, is be; but be is equal to the chord 
Oa cut from OR by the auxiliary circle, as can be seen by draw- 
ing the lines P c , Pob, and P x a (all of which are perpendicular 
to OR because they are drawn in semicircles) and further by 
producing Pc to e and drawing P e parallel to OR; for P e is 
equal to be and the triangle P<JPe and OP x a are evidently equal. 
A convenient construction for the diameter of the auxiliary 
circle is to draw an arc from O with a radius equal to PPq and 
another from P with a radius equal to OPq, which arcs will inter- 
sect at P x , and we may draw the parallelogram OP x PPq. A 
second auxiliary circle, OP J, drawn below the axis XX', shows 
the displacement of the plate to the left, from the middle of the 
main valve. 

It must be remembered that OP x is not an eccentricity and 
that the angle P x OY is not an angular advance, and in general 
that the auxiliary circle is only a device for solving problems, and 
represents no part of the engine when completed. 

The essential parts of the diagram given in Fig. 3 are repeated 
in Fig. 4, together with the lap-arc nn' for the main valve and 
the clearance-arcs //' and l"V" for the plate. When the displace- 
ment of the plate to the right from the middle of the valve is 
equal to the clearance /, the edge of the plate comes to the edge 
of the port as indicated by Fig. 1, PI. XXVII, and we have either 
cut-off or readmission. Cut-off by the plate comes at OR and 
readmission at OR'; at the first position the plate is moving to 
the right relative to the main valve to close the port, and at the 



DOUBLE VALVE-GEARS. 99 

second it is moving relatively to the left and reopens the port. 
The cut-off by the main valve comes at OC so that a double 
admission does not occur; the valves are then in the position shown 
in Fig. 2, PI. XXVII. On the other stroke of the engine, cut-off by 
the plate comes at OR!" and readmission at OR", but these events 
belong to the left-hand edge of the plate and have nothing to do with 
the right-hand end of the cylinder, so that, in particular, we need 
not be concerned as to whether the readmission is early enough, 
as was the case for the valve in a separate valve-chest 

Meyer Valve. — A double valve-gear, known as the Meyer 
valve, is shown by Fig. 2, PI. XXVIII. The cut-off valve is 
made in two parts on a valve-spindle with a right and left screw, 
i^so that the position of the plates may be adjusted by rotating 
a) the valve-spindle; thus the clearance may be changed, and 
> consequently the cut-off may be varied. In order that this may 
be done while the engine is running, there is a swivel- joint in the 
valve-spindle between the valve-rod head and the valve-chest, 
and the tail of the valve-spindle is carried through the head 
end of the valve-chest, where it reciprocates through a hand- 
wheel as shown by Fig. 1 ; the valve-spindle is squared at the 
end so that it may be rotated by turning the hand-wheel. 

An inspection of Fig. 4, PL XXVI, shows that the cut-off 
may be lengthened by increasing the clearance and that it may 
be shortened by decreasing he clearance. In order that the 
cut-off may come at a given crank-position, such as OR, the 
clearance must be equal to the chord cut by that line from the 
auxiliary circle. If the clearance becomes equal to zero so that 
the edge of the plate is on the edge of the port when both are 
in mid-position, then the cut-off comes at OR and the readmission 
is at a position diametrically opposite. If an earlier cut-off is 
desired, the plates must be pushed still farther out so that they 
have a lap; such a lap will be drawn across the other valve- 
circle, as at mm' , and will indicate that cut-off comes at OR\ and 
readmission at OR 2 . 



N? 



loo VALVE-GEARS FOR STEAM-ENGINES. 

Design of a Meyer Valve. — The main valve as shown by Fig. 2, 
PL XXVIII, has a steam-lap of half a inch, and is moved by 
an eccentric with an eccentricity of i| of an inch; the exhaust- 
lap is zero. It is set with -^ of ah inch lead. With these dimen- 
sions the valve-circle OP in Fig. 3 can be drawn, and the cut-off 
will be found to occur at OR c ; corresponding, with harmonic 
motion, to 0.89 of the stroke of the piston: 

The steam-port in the valve-seat is | of an inch wide, and 
the steam-port through the main valve may be taken to be | 
as much, or J of an inch. The diameter of the auxiliary circle 
may be assumed to be one inch. With an eccentricity of if of 
an inch for the cut off valve-eccentric, the parallelogram PP OP Z 
may be drawn locating both the auxiliary circle OP x and the 
diameter OP of the circle, showing the absolute displacements 
of the cut-off valve. The cut-off valve-eccentric has the angular 
advance YOPq, equal to 55 ; it is convenient to know this angle 
approximately in setting the valves. The dimensions for OP x 
and OPq are chosen by trial to give a convenient location of the 
auxiliary circle, with its diameter placed beyond OR c to avoid 
the possibility of a double admission. 

The largest clearance is 01 =M of an inch; the least clear- 
ance, or the greatest lap, will depend on the earliest required 
cut-off. Let it be assumed that the earliest cut-off shall be at 
ORi, corresponding to a piston-displacement Xa = \ of the stroke, 
for harmonic motion; then the cut-off valve must have a lap 
equal to 01" = OV" = h of an inch, nearly. 

The lower face of the main valve is laid out as for a plain 
slide-valve, but with the additions demanded by the passage 
through it. The least width of bridge is equal to the eccentricity 
less the sum of the lap and the width of port, or ij— (£■+!) 
= I of an inch ; , the width used is \ of an inch. In like manner 
the width of the exhaust-space is i| + f— |=if of an inch; the 
width used is 2X£f =i| of an inch. In order that the edge c 
of the passage through the valve may not reduce the passage 



DOUBLE VALVE-GEARS. ioi 

through the port to less than \ of an inch, the distance ac is 
made 1^ + ^ = 2 inches; this feature is frequently overlooked and 
dc is carelessly made equal to e}. In order that the edge g of the 
valve shall not come to the edge b of the port, the distance bg is 
made ij+| = if of an inch. The valve-face is cut away at a 
point h, 1 \ of an inch from g, thereby giving an overtravel of 
I of an inch. In order that the space ejdc may be made small, 
the height of the exhaust- space is made only f of an inch, a dimen- 
sion that is probably too small to give a perfectly free exhaust. 

The length of the cut-off valve must be enough so that steam 
cannot leak past the inside edge when the valve is set to give the . 
earliest cut-off and when it also has its maximum displacement. 
In Fig. 2, PI. XXVIII, the position of the valve to give cut-off 
at | of the stroke is shown by dotted lines; its lap is A of an 
inch, and its left-hand edge k is 1 +■§- = i|- of an inch from e. 
The length of the cut-off valve is i|- + f +^ = 2- 1 J 6 - inches. The 
cut-off valve is shown in section with a clearance of M of an 
inch, which is proper for giving the longest cut-off coincident 
with that of the main valve; its left-hand edge is 2^+^ = 3^ 
inches from the edge / of the port ef; the distance of the edge / 
of the port from the middle of the valve is made 3^ inches. 
The half-length of the main valve, over all, is made 4J inches, 
and provides an overtravel of | of an inch for the cut-off valve 
when set to give the earliest cut-off. The cut-off valve has an over- 
travel only when the cut-off comes early in the stroke; the main 
valve might be somewhat shorter, but an attempt to provide over- 
travel for the cut-off valve when it gives a long cut-off will make 
the main valve too short. 

The valve-spindle is provided with a right-and-left-hand 
screw, of which the right-hand part is shown. The thread 
should be cut only far enough to give the desired variation of 
cut-off, or some other stop should be provided in order that 
the engine attendants may not move the cut-off valve too far 
out, and so get a leakage or even admission of steam past the 



102 VALVE-GEARS FOR STEAM-ENGINES. 

inner edge. The spindle is shown in two parts, joined by a 
right-handed screw and circular nut or sleeve with pins to prevent 
the joint from jarring loose; this arrangement is to facilitate the 
assembling of the valve-gear. 

In this design the exhaust-lap is made zero and the compres- 
sion and release are neglected ; in practice these features should 
receive the same attention as is accorded to them in designing 
a plain slide-valve. Again, the irregularity of the piston-motion 
due to the angularity of the connecting-rod has been ignored, 
and the clearance (or lap) of the cut-off valve has been made 
the same at both ends. This method is commonly followed in 
practice, but by using proper pitches for the threads on the valve- 
spindle the cut-off may be equalized at two points of the stroke, 
for example at | and at J stroke, and will then be found to be 
more nearly equal for all parts of the stroke, except for long 
cut-off, when inequality is of less importance. / 

Meyer Valve with Cut-off at Inside Edge. — Sometimes the 
Meyer valve is designed to cut off at the inside edge, as shown 
by Fig. 4, PL XXVIII. It is then convenient to consider that 
the valve has a lap ab which diminishes as the cut-off is lengthened, 
and which may become zero and finally change to a clearance, 
shown by ac when the valve is in the position indicated by dotted 
lines. The eccentric is given a negative angular advance, i.e. it 
is set somewhat less than 90 ahead of the crank. 

In Fig. 4, PL XXVII, the main valve-circle is OP, giving 
a cut-off at OR, with a lap On = On". Let it be assumed that 
the earliest required cut-off is at OR 2 , and that the latest read- 
mission must be at OR\] then the auxiliary circle may have 
its diameter at OP x , on a line bisecting the angle RiOR 2 . The 
diameter of the valve-circle for showing the absolute displace- 
ment of the cut-off valve will be found at OP by completing 
the parallelogram PP X OP ; the eccentricity for the cut-off valve- 
eccentric is OPq, and the negative angular advance is YOP . 
The auxiliary circle may be placed lower down, thereby giving 



DOUBLE VALVE-GEARS. 103 

an earlier readmission and at the same time a larger eccentricity, 
but it cannot be placed higher up. There is no danger of a 
double admission of steam at a long cut-off, in which regard this 
form of valve differs from the ordinary Meyer valve. 

The Meyer valve is sometimes applied to reversing-engines, 
like marine or locomotive engines, and in such case it is desirable 
to have the cut-off valve thrown entirely out of action in the 
backing motion of the engine because it is impossible to design 
a motion that shall be satisfactory in both forward and backing 
gear, and engines of such type habitually run forward and only 
back occasionally. The valve should then be designed for 
forward motion only and as such a valve is likely to give a very 
bad distribution of steam when backing, the plates may be 
drawn back so far that they will not have any effect in that 
gear. 

Cut-off Valve with Loose Eccentric. — Let the cut-off valve 
receive motion from an eccentric which may turn freely on the 
engine-shaft and which is under the control of a shaft-governor; 
let the clearance of the cut-off valve be unalterable: then the 
cut-off can be varied by changing the angular advance of the 
cut-off eccentric. 

In Fig. 3, PL XXVII, the main valve-circle is OP, and with 
a lap on = on' the cut-off by the main valve occurs at OR c . The 
cut-off eccentric may have its angular advance changed from 
YOPq to YOPq, then the auxiliary circle may change from OP x 
to OP J. When the position of the diameter OP of the circle, 
showing the absolute displacement of the cut-off valve, is known, 
the auxiliary circle may be located by completing the parallelo- 
gram PPqOP x ; or the centre C x of the auxiliary circle may 
be located by completing a parallelogram CCqOC x on the half- 
diameters OC and OCq of the main valve-circle and the cut-off 
valve- circle. Since the side CC X of this last parallelogram is 
equal to OCq = %OPq, it is at once apparent that the locus of the 
centre of the auxiliary circle is the dotted circle C X C X drawn from 



104 VALVE-GEARS FOR STEAM-ENGINES. 

the centre C of the main valve-circle, and with a radius equal to 
half the eccentricity of the cut-off eccentric. Again, since PP X 
is equal to OPq, the locus of the end of the diameter of the auxili- 
ary circle is a circle drawn from P as a centre and with a radius 
equal to the eccentricity of the cut-off eccentric. The locus of 
the end of the diameter of the auxiliary circle is the more con- 
venient for use in solution of problems. 

Let it be assumed that the cut-off shall vary from the crank- 
position OR c , coincident with the cut-off by the main valve, to 
ORu corresponding to J stroke for harmonic motion. Assume 
the clearance of the cut-off valve and draw the circle IV I" . Erect 
a perpendicular SC X at the middle of the line 01" ; it will intersect 
the locus C X C X at C z , the centre of the auxiliary circle that will 
give a cut-off by the cut-off valve coincident with the cut-off by 
the main valve. In like manner, erect a perpendicular at the 
middle of the line 01'; it will locate the centre CJ of the auxiliary 
circle that gives a cut-off at OR 1} corresponding to \ stroke. 
By drawing perpendiculars from I" and I', the ends of the 
diameter OP xf and OP J' would have been found. 

In designing a valve-gear of this type, the clearance of the cut- 
off valve may be chosen, usually somewhat larger than the width 
of the port in the main valve; and then' the auxiliary circle for 
maximum cut-off may be given such a diameter that a satisfactory 
action may be had in that gear. The eccentricity of the cut-off 
eccentric will be found by completing the parallelogram in the 
usual way; should the result be an undesirable dimension it may 
be modified, since the diameter of the auxiliary circle may be 
varied to a considerable extent. Finally, the auxiliary circle to 
give the earliest cut-off may be found by the process just stated; 
it is liable to have a large diameter, and the travel and wear of the 
cut-off valve is likely to be excessive. In the figure the auxil- 
iary circle which gives a cut-off at \ stroke is one-third larger 
than the main valve- circle, and it would be still larger for a 
shorter cut-off. It may be seen that the maximum diameter of 



DOUBLE VALVE-GEARS. 1 05 

the auxiliary circle is equal to the sum of the eccentricities for 
the two eccentrics. 

If this gear is used with a shaft-governor, the cut-off by the 
main valve will commonly be earlier than that shown in Fig. 3 
— a circumstance that will make the design of a satisfactory 
gear easier. Moreover, it may be possible to limit the maxi- 
mum cut-off to half-stroke or less, even though the main valve 
gives a cut-off beyond half-stroke; in that case the valve mechan- 
ism must be so arranged that the cut-off valve cannot act beyond 
the assumed range of cut-off, otherwise a double admission may 
occur. These observations are applicable also to the next type 
of valve-gear. 

Cut-off Valve with Constant Travel. — It is desirable that a 
valve shall overtravel its seat in order that the seat and the face 
of the valve may wear evenly and remain true. This is seldom 
possible for all grades of cut-off with a Meyer valve of common 
proportions, or with a cut-off valve under the control of a loose 
eccentric. It has been seen that the design of the cut-off valve is 
conveniently begun by choosing the diameter and position of the 
auxiliary circle; it will be found that the design of a double 
valve-gear for a given purpose may be worked out by first 
finding how the auxiliary circle must be located or changed to 
give the desired action, and then finding how the cut-off eccentric 
must move to produce such an auxiliary circle. 

Suppose that the auxiliary valve-circle is to have a constant 
diameter, and that the variation in cut-off is to be produced by 
swinging the auxiliary circle around the origin O, Fig. 1, PI. 
XXIX, from the position OP x to OP J. With a clearance equal 
to 0l = 0l' = 0l", the first-named auxiliary circle will give cut- 
off at OR c , coincident with the cut-off by the main valve; and 
the other auxiliary circle, OP J, will give cut-off at OR\, corre- 
sponding to \ stroke. The diameters of the cut-off valve-circles, 
showing absolute displacements, are OP and OP ', found by 
completing the parallelograms PP X OP and PP x 'OPq. It is 



106 VALVE-GEARS FOR STEAM-ENGINES. 

evident that the locus of the point P is the circle PqPq' drawn 
from P as a centre and with a radius equal to the diameter of 
the auxiliary circle. 

The arrangement of the eccentrics for this type of valve- 
gear is shown by Fig. 2, PI. XXIX. The centre of the engine- 
shaft is at O; on the shaft is the fixed eccentric centred at E y 
for giving motion to the main valve; the cut-off eccentric is 
carried by the main eccentric, and is shown by the full-line circle 
with its centre at Eq, corresponding to OPq in Fig. 1, while 
the dotted circle shows it with the centre at E , corresponding 
to OPo in Fig. 1. The cut-off eccentric may readily be placed 
under the control of a shaft-governor. 

The main valve represented by Fig. 3, PI. XXIX, has a lap 
of \ of an inch, and is moved by an eccentric having i\ of an 
inch eccentricity, and is consequently a reduplication of the 
main valve for the Meyer valve-gear shown on PL XXVIII, at 
its lower surface; the top is of course laid out after the cut-off 
valve has been designed. The main valve-circle has its diameter 
at OP, Fig. 1, and the cut-off by that valve occurs at OR c . The 
cut-off valve is a double-ported or gridiron valve, each of the 
ports being \ of an inch wide. The clearance of the cut-off 
valve is assumed to be f of an inch, represented by the circle 
//'/" As the auxiliary circle swings toward the right to give an 
earlier cut-off, the readmission moves through the same angle 
toward the line OR c , the crank-position at cut-off by the main 
valve; and it is at once evident that the readmission must not 
be earlier than OR c , otherwise a double admission may occur. 
The smallest admissible auxiliary circle will have its centre on 
the line 0,5 bisecting the angle R\OR c , and it will pass through 
the points V and I" at the intersection of the clearance-circle by 
the lines 0R\ and 0R C . The diameter chosen for the auxiliary 
circle is f of an inch, or twice the clearance of the cut-off valve. 
The extreme positions, OP J arid 0P X , of the auxiliary circle are 
so located that they shall pass, one through V and the other 



DOUBLE VALVE-GEARS. 107 

through l"\ they give cut-off at ORi and at OR c . The corre- 
sponding diameters of the cut-off valve-circles are OPq' and 
OPq, found by completing the parallelograms P x PP Q and 
P x 'PPqO. The cut-off eccentric is mounted on the main eccen- 
tric and has an eccentricity, referred to that eccentric, of f of 
an inch, equal to the diameter of the auxiliary circle. 

In laying out the cut-off valve and the upper surface of the 
main valve, it is convenient to begin in Fig. 3 by placing the 
port a in a convenient position near the exhaust- space e. From 
the right-hand edge of this port lay off f of an inch to c, the left- 
hand edge o the outer part of the cut-off valve; this is equal 
to the greatest displacement of that valve, and insures that the 
edge c shall not overrun and contract the port a. From c lay 
off somewhat more than f of an inch, in this case if of an inch 
to the left-hand edge of the port b; this gives the necessary length 
of the bar cd in order that leakage may not occur past the edge 
c at the maximum displacement toward the right. The clearance, 
I of an inch, is laid off from the right-hand edge of the port b, 
* to determine the edge d of the bar cd. The inner right- 
hand bar is made as wide as cd. The left-hand half of the 
main valve and the cut-off valve is a counterpart of the right- 
hand half. 

The cut-off valve-spindle takes hold of a lug on one of the 
bars of the gridiron cul-off valve; and the main valve-spindle 
passes through a tube or passage bored out through the middle 
of the main valve. 

To Set a Double Valve-gear. — Set the main valve to give 
equal lead; the cut-off by that valve has little influence on the 
running of the engine, and requires little or no attention. If 
the cut off valve is designed to cut off at a definite point when 
the engine is running under normal conditions, equalize the 
cut-off by that valve at that point. If the load on the engine 
and the cut-off are variable within a limited range, the valve 
should be set to give the least irregularity within that range;. 



Jo8 VALVE GEARS FOR STEAM ENGINES. 

k will usually be sufficient to equalize the cut-off for the middle 
of the range. If the range of cut-off is wide, it will often be im- 
possible to get a good action for the entire range, and then it will 
be advisable to equalize the cut-off for some early point in the 
stroke of the piston. It has already been pointed out that the 
Meyer valve may have the cut-off equalized at two points of the 
stroke by using unequal pitches for the screws on the valve. 
spindle. 



CHAPTER VI. 
DROP CUT-OFF VALVE-GEARS. 

In this chapter there will be given descriptions of a few 
special forms of valve-gears, selected, partly at random, from 
the large variety of such gears employed by the builders of auto- 
matic cut-off stationary engines. All are of the four-valve type 
of valve-gears, and all give a drop or disengagement cut-off. A 
description and analysis of these few forms will enable the 
student to analyze and understand other gears of similar types. 

Brown Engine Gear. — Fig. i, PL XXX, gives a section 
through the head-end valves and valve-chests of the Brown 
engine; the crank- end valves and gears are a duplication of 
those for the head end. The admission-valve V is a five-ported 
gridiron valve on a vertical valve-seat, and the exhaust- valve is 
a three-ported gridiron valve on a horizontal seat. Both are 
controlled by valve-gears on the shaft O, which is driven by the 
engine-shaft through a pair of equal bevel-gears and which makes 
one revolution for each revolution of the engine. It is clear 
that four such valves might be driven directly by one eccentric 
on the engine-shaft, or by four eccentrics on the shaft O, and 
that in such case the four valves would be equivalent to one 
plain slide-valve, and would be designed by the principles laid 
down in the first chapter. 

The eccentric E, which moves the steam valve-gear, is set 
to one side of a vertical through e, so that it gives a slow up- 
ward motion to the lever fe. The toe of the lever Je catches 



no VALVE-GEARS FOR STEAM-ENGINES. 

under (he edge of the latch L, and lifts the valve V through the 
spindle SV. When the tail of the latch strikes the pin d, the 
valve is disengaged from the lever Je, and it falls shut; a dash- 
pot P checks the fall of the valve and prevents jar. The pin 
d on the arm bd is under the control of the governor through 
the horizontal shaft b. It is commonly said that the governor 
on an engine with a detachment cut-off gear has only the light 
duty of setting the stop (in this case the pin d) that unlatches 
the gear and releases the valve; the friction of the governor 
and the attached parts is, or should be, small. Most such gears 
throw a shock on the governor, tending to disturb it and make 
it race when the cut-off valve is released; and the governor 
should be sufficiently powerful to resist the shock. In this 
gear, when the tail of the latch L strikes the pin d, the shock 
tends to open the later and to throw the pin toward the left; 
both will yield, but the motion of d, and consequently of the 
governor, is slight. 

The exhaust-valve is moved by the earn C, which consists 
of a groove, in the face of a disk, in which works a roller on 
the end of the lever trS'. The end S' of the lever is slotted and 
provided with a block to avoid bending the valve-spindle V'S'. 
The action of this cam is equivalent to that of an eccentric, 
-except that there are periods of rest when the valve is open or 
shut. Fig. 2 shows two ways of laying out such a cam; it is 
intended to show general principles only, and would require 
some modification to fit it to the engine shown by Fig. i. Let 
it be supposed that the cam acts directly on the end of a hori- 
zontal valve-spindle, such as V'S', Fig. i, and that its centre is 
on a prolongation of the path of the valve-spind'e. Suppose, 
further, that the cam turns toward the left, and that the valve 
shall begin to open when the line Od is horizontal, and be wide 
open when Ob is horizontal. To give a uniform motion to the 
cam, make the curve i, 3, 7 an arc of an Archimedean spiral; 
this is done by dividing the angular space bd and the linear space 



DROP CUT-OFF VALVE-GEARS. m 

I '7 into the same number of equal parts, and by drawing inter- 
secting arcs and radii, 6'6, 06, 5^5, O5, etc., as shown. The 
cam from b to c is a circular groove, so that the cam remains at 
rest till the line Oc comes into coincidence with the path of the 
valve-spindle. The groove from the line Oc to the line Oa is so 
designed that is gives a harmonic motion. On the line i'7 a 
semicircle is drawn, and its arc and the angular space cOa are 
divided into the same number of equal parts; arcs and radii 
are drawn intersecting at 1, 2, 3, etc. Finally, the cam from 
Oa to Od is a circular arc, giving a period of rest. The second 
construction, giving harmonic motion, is to be preferred for 
heavy valves having a rapid motion, in order that they may 
start and stop easily and quietly; fo valves that move 
slowly and have a large frictional resistance, the first con- 
struction may be preferable, but the cam should be modified 
by rounding the corners at 1 and 7, to avoid a shock at starting 
and stopping. The positions of the lines Ob, Od, Oa, and Oc 
may be chosen by the designer so that the time and rate at which 
the valve opens and shuts may conform to the requirements of 
his design and to the dictates of his judgment and experience. 

The cam in the figure has a symmetry with regard to the 
axes xx' and yy' that suggests the resemblance of its action to 
that of an eccentric. 

It is neither necessary nor customary to balance valves of 
the type used on the Brown engine, for they have little pressure 
on them to produce friction when they are moving, and when 
they are shut they are at rest. It is usual and advisable to set 
the exhaust-valve to give compression nearly up to the steam- 
pressure in the steam-chest, so that the pressure under the steam- 
valve is nearly equal to the pressure on it at admission. The 
valve drops shut at cut-off, and after it is at rest the steam-pres- 
sure in the cylinder is reduced by expansion. The expansion is 
carried down to within a few pounds of the back-pressure, so 
that at release the pressure on the exhaust- valve is not excessive; 



112 VALVE-GEARS FOR STEAM-ENGINES. 

at compression the pressure in the cylinder rises after the valve 
is at rest. 

A feature common to many detachment cut-off gears can be 
well shown by reference to Fig. i, PL XXX. Let it be supposed 
that the eccentric E has no angular advance, and that the valve 
has no lead; then the valve will open at the beginning of the 
stroke, and will have its greatest displacement, provided that 
it is not sooner released, when the piston is at or near half-stroke. 
If the latch has not then struck the pin d, it will not strike it at 
all, and the valve will remain connected to the gear, and will 
close at or near the end of the stroke. It is also evident that giving 
angular advance to the eccentric and lap to the valve will limit 
still further the range of cut-off. In this gear, however, the cut- 
off may be continued beyond half-stroke by giving a negative 
angular advance to the eccentric and a clearance to the valve. 
If an engine with a detachment cut-off that is limited to the 
first half of the stroke is overloaded, there is a liability that a 
failure to cut off will occur, in which case the sudden increase 
of work due to the steam following the piston to the end of the 
stroke will make the engine run very irregularly. 

Corliss Valve-gear. — Of all types of detachment valve-gears, 
that invented by Corliss has been most widely known and has 
received the most favor. A modification of this gear designed 
by Mr. Edwin Reynolds is shown by Plate XXXI, which repre- 
sents the valve-gear on the intermediate cylinder of the triple- 
expansion engine in the Engineering Laboratories of the Massa- 
chusetts Institute of Technology. 

The Corliss type of engine has two steam-chests, S for the 
supply and R for the exhaust; the latter is separated from the 
cylinder in order that the exhaust-steam may not chill it. 
This arrangement produces a somewhat rectangular casting 
containing the steam-chests and the cylinder, at the four corners 
of which are placed four valves, two of which, V and v, are ad- 
mission- or steam- valves, and the other two, W and w , are exhaust- 



DROP CUT-OFF VALVE-GEARS. 113 

valves. The valve-seats are bored cylindrical and the faces of 
the valves are turned to fit; the valves bear on half a circle or 
less, and are so connected to the valve-spindles that they may 
follow the valve-seats without cramping the valve-spindles. The 
valve-spindles, which are at right angles to the axis of the cylinder, 
project through stuffing-boxes and carry cranks on the ends, by 
means of which the valves are turned on their seats. The exhaust- 
valves W and w have their valve-cranks WD and wd connected 
directly to pins A and a, in a wrist-plate O, which receives a 
harmonic oscillation from an eccentric on the engine-shaft. The 
admission-valves take steam on their inner edges as shown at V, 
and their cranks carry blocks as shown at the crank-end. In 
the figure a section is taken just behind the crank Vh, which is 
represented by a dotted line only, in order to show the disen- 
gagement-latch zTh, which engages the block h and is carried 
by the bell-crank lever EVT; the lever EVT is connected by 
the link EB to the wrist-plate. The latch is opened when the 
finger Tz strikes the stop x on the ring xq; the ring is placed 
under the control of the governor through the cut-off rod NM 
and the double-armed bell-crank lever Mlm, to which the gov- 
ernor-rod is attached at I. The linkage made up of the valve- 
crank, valve-rod, and wrist-plate, for example Oadw, is designed 
to give a slow motion when the valve is closed, and a rapid motion 
when opening or closing. The figure shows the wrist-plate 
and valves in mid-position, the eccentric being erect. The ex- 
haust-valve w has its edge on the edge of the port; its crank 
moves through the angle dwd 2 , while the wrist-plate oscillates 
through the angle aOa 2 , but that crank has only the angular 
motion dwd x , while the wrist-plate moves through the angle aOa,\ = 
aOa 2 . The admission-valves have a similar action as shown at 
e\ve 2 . If it be supposed that the governor-balls are at their 
lowest position (at which the disengagement-gear does not act), 
it will be seen that this gear differs from the plain slide-valve 
gear in two points: first, it has four valves; and second, these 



H4 VALVE-GEARS FOR STEAM-ENGINES. 

valves have a more favorable action when opening and closing, 
on account of the linkages just described. 

From a pin at g in the crank Vh, a dash-pot rod represented 
by the line gi leads to a vacuum dash-pot shown by Fig. 2. This 
dash-pot has two pistons, p and P; the lower piston fits nicely 
in a closed cylinder from which air is excluded ; the upper piston 
works in a larger cylinder that is open to the atmosphere through 
a series of orifices i, iy, and i 2 and the pipe O. When the valve- 
crank Vh, Fig. 1, is raised, it lifts the double piston Pp and a 
partial vacuum is formed under p, while air enters freely through 
the orifices i, i\, «2> to the annular space under the piston P. 
When the valve is disengaged, the weight of the dash-pot and the 
dash-pot rod, aided by the yacuum under the piston p, closes the 
valve promptly; while the air under the piston P acts as a buffer 
and prevents a shock. The pipe O is provided with a hollow 
plug as shown, by aid of which the escape of air through the 
orifices i, i\, and i% may be regulated. 

A large number of detachment-gears have been devised and 
used by Corliss, and by others who have used this type of valve- 
gear. The one shown by Fig. 1, PI. XXXI, was invented by 
Mr. Reynolds and has the advantage that the latch mechanism 
is centred on the same axis as the cut-off stop; consequently the 
finger z always strikes the stop x at the same angle, and the 
same force is required to disengage the cut-off valve. The block, 
when disengaged, slides along the plate y. On the return motion 
the plate y slides over the block till it can snap on to it, under the 
influence of the spring st. 

It is customary to give a small lap to the steam-valves* con- 
sequently, as with a plain slide-valve, the eccentric has a small 
angular advance. With such an arrangement the eccentric 
centre will be on the line of dead-points, and the valves will have 
their greatest displacement when the crank has moved through 
90 less than angular advance, and before the piston is at half- 
stroke. If the detachment-gear has not been released before 



DROP CUT-OFF VALVE-GEARS. 115 

the valve has received its greatest displacement, the valve will 
not be disengaged at all, but will remain under the control of the 
linkage connecting it to the wrist-plate; and cut-off will occur 
near the end of the stroke, and will be determined by the lap and 
angular advance as with a plain slide-valve. It is therefore 
evident that the range of cut-off for the ordinary form of the 
Corliss gear is from the beginning of the stroke to half-stroke or 
less. When a longer cut-off is desired, for example on the low- 
pressure cylinder of a compound engine, two wrist-plates may be 
used; one wrist-plate, moved by an eccentric with a small angular 
advance, has control of the exhaust-valves, and gives release and 
compression near the ends of the stroke; the other wrist-plate is 
moved by an eccentr'c with a negative angular advance, and has 
control of the steam-valves which have a clearance instead of a 
lap : with this device the range of cut-off may be extended beyond 
half-stroke 

Expertness in laying out Corliss valve-gears can be obtained 
only by experience, with good examples for models. The steam- 
port may be made from Yt to A of the area of the piston, and 
the exhaust -port may be made T V to T y of that area. The ex- 
haust-valve commonly has no lap; the admission- valve has a 
small lap, \ of an inch, in Fig. 1, PL XXXI. In that figure 
ve is the mid-position of the steam valve-crank, and e'e\ is the 
maximum valve-displacement, equal to the lap plus the port- 
opening; ve x is the extreme position of the valve-crank. The 
points b and &i are found by intersecting the arc b\b 2 by arcs 
drawn from e and e x with a radius equal to the length of the link 
BE. The arc bb 2 is made equal to bb u and ve 2 , the extreme 
position of the crank when the valve is shut, is found by inter- 
secting the arc eie 2 by an arc drawn from b 2 with a radius equal 
to the length of the link. The linkage Oadw is laid out in a 
similar way, except that the angle aOa x is from necessity equal 
to bOb. The lengths of the valve-cranks and the radii from 
the centre of the wrist-plate to the pins a and b depend partly 



n6 VALVE-GEARS FOR STEAM-ENGINES. 

on the proportions of the engine and partly on the habit and 
discretion of the designer ; the longer they are, the less will be the 
force exerted on the links, ad and be, and on the pins which they 
connect. The angle veb should be nearly a right angle, so that 
a rapid opening of the valve may be obtained. The pin C in 
the wrist-plate receives motion from the eccentric either directly 
or through a carrier or single-armed rocker that magnifies the 
throw of the eccentric in about the proportion of i : i J. The 
chord of the arc C\C 2 , through which C swings, is not longer than 
the radius OC in order that the angle C\OC may not be more 
than 30 . The linkages Oadw and Obev are to be laid out by 
trial to give as nearly as may be the desired motion to the valves. 
It will be noticed that the radius Oai and the link a x d x are in one 
straight line at the extreme position of the exhaust- valve; and 
in like manner Ob 2 and ^2 are in one line; should the linkages 
be carried beyond these positions, a double oscillation would be 
given to the valve-cranks, which is considered to have a bad 
appearance. The system of rods and levers connecting the rings 
xqN and vn with the governor is laid out so that the cut-off may 
come at the beginning of the stroke when the -governor stands at 
the top of its range of motion, and when the governor is at the 
bottom of that range the cut-off may come at or after half-stroke, 
i.e. the valve will not be released Though it is not always done, 
it will be advisable for an inexperienced designer to draw the 
valve-ellipse for the steam- and exhaust-valves The ellipse, 
or more properly the oval, will have a form like that shown by 
Fig. 3. The valve will be found to open rapidly and to nearly 
its full width early in the stroke of the piston. A line nn' drawn 
at the distance xn, equal to the lap, from the axis xx' , will show 
that the cut-off occurs near the end of the stroke. The valve 
will be found to be nearly at rest during the greater part of the 
time when it is closed. 

The steam-valve is disengaged when the latch holding it is 
released, but cut-off does not occur till the- edge of the valve 



DROP CUT-OFF VALVE-GEARS. 117 

comes to the edge of the port, which is an appreciable time later. 
In Fig. 3, PI. XXXI, let a represent the point of disengagement; 
then, under the influence of the dash-pot, the valve falls with an 
accelerated velocity till it is checked by the air-cushion in the 
dash-pot. Representing the motion of the piston by abscissae, 
and the motion of the valve by ordinates (just as in drawing 
the ellipse), the action of the valve in closing may be represented 
by the dotted line abc; the point of cut-off is represented by b 
at the intersection of this line and the lap-line nn' . The piston- 
displacements may be readily found from the dimensions of the 
engine and its speed of rotation, but the forces acting on the 
valve and its resistances cannot be estimated. The forces are 
the weight of the dash-pot and attached parts, together with the 
pressure of the atmosphere on the area of the piston p. The 
resistances are friction of the valve, of the dash-pot, and of other 
parts of the mechanism, and the varying pressures under the 
pistons P and p; the pressure under P is due to the escaping 
air, and under p to the air beneath it when at its lowest 
position Though the line abc cannot be determined by cal- 
culation or construction, it may be found experimentally by 
an apparatus described on page 7 for making an engine draw 
its own ellipse. The action of the valves of a Corliss engine 
is commonly inves igated by aid of a steam-engine indicator; if 
the indicator diagram shows a sharp cut-off, and if the other 
features are good, the action of the valves is considered to be 
satisfactory. 

Putnam Valve-gear. The Putnam engine has four double 
poppet-valves, two for admission and two for exhaust. Plate 
XXXII shows a section through one of the admission- valves 
and its valve-gear XX' s a casting bolted onto the cylinder- 
casting. The space SS' is the steam-chest, and the space P 
leads to the cylinder. The two valves V and V\ are made of 
composition and, when closed, rest on composition seats let 
into the casting. The seat of ihe valve V is large enough to 



Ii8 VALVE-GEARS FOR STEAM-ENGINES. 

pass the valve Vi, so that the valves may be readily withdrawn 
through the hand-hole H. The unbalanced pressure, which must 
be overcome when the valve is opened, is that on the excess 
of the area of the upper valve over that of the lower valve. The 
valve-spindle ab is made of iron to avoid unequal expansion 
and consequent leakage; for, if the distance between the valves 
is not exactly the same as the distance between the valve-seats, 
one or other of the valves will not come properly to its seat. 

The valve-spindle ab is stepped into a frame mn, shown 
in section. The arm gq is loose on the shaft and under the 
influence of the spring Ik presses on the frame mn; a pin p' is 
interposed to reduce friction. The other arm, gf, of the bell- 
crank lever carries the cam-lever }e, which acts on the frame mn 
through the interposed sliding-block d and the pin p; this cam- 
lever is driven by the double cam C. This cam C, and three 
others, one for the other steam-valve and two for the exhaust- 
valves, are carried by a shaft which is parallel to the axis of 
the cylinder and which is driven from the engine- shaft through 
bevel-gears, so proportioned that the cam-shaft makes one turn 
for two revolutions of the engine. The figure shows the cam 
in contact with the cam-lever, and the valves on their seats; 
the engine is consequently at admission. As the engine moves 
forward, the cam-shaft turns as shown by the arrow and raises 
the valves, giving admission of steam, till the cam slides past the 
corner y of the cam-lever; the valve is then released and falls 
shut under the influence of the spring kl. The governor-rod 
takes hold of the pin h at the end of the lever gh. When the 
speed of the engine increases and the governor rises, the lever 
hg is thrown down and the cam-lever ef is pushed to the left, so 
that the cut-off comes earlier. No shock is thrown on the 
governor when the valve is released, but as the edge of the cam 
is rounded to avoid cutting the cam-lever, there is a tendency 
to disturb the governor which the governor must be able to 
resist. Should the valve fail to close for any reason, the other 



DROP CUT-OFF VALVE-GEARS. 119 

end of the cam will strike on i and close the valve before the 
engine makes a return stroke. 

The exhaust-cam is shown at A. At each end the cam is 
cylindrical, so that it holds the exhaust-valve open till near the 
end of the stroke. The exhaust cam-lever is not placed under the 
control of the governor, but can be set to give a fixed compression. 

Gaskill Valve-gear. — One of the steam-valves for the high- 
pressure cylinder of the Gaskill horizontal pumping- engine, and 
part of the valve-gear, are shown on Plate XXXIII. The valve 
is shown in section by Fig. 2, and the seat is shown in section 
and half-plan by Figs. 2 and 3. The valve is of the Cornish 
type and differs from the double poppet-valve only in detail. 
Like that valve it consists of two valves joined together, the 
inner valve being small enough to pass through the valve-seat 
of the outer or upper valve. The unbalanced pressure to be 
overcome to open the valve is that on the difference of areas 
of the two valves. When open, both valves give admission 
of steam. The valve-seat £ is bolted to the cylinder-casting, 
and a passage leads directly to the end of the cylinder. The 
valve is covered by a small cylindrical valve-chest; there are 
two such chests, one at each end of the cylixder, supplied by 
a branched steam-pipe. 

The valve-gear is shown by Fig. 1, in which E is an eccentric 
on a shaft parallel to the axis of the cylinder, and driven from 
the engine-shaft through equal bevel-gears, so that it makes one 
turn for each revolution of the engine. The eccentric-strap has 
the cut-off toe a at one end and a lug b at the other. From b 
the rod bC leads to one end of an equal-armed lever, and the 
valve- spindle d is hung from the other arm; the distance be- 
tween the rod C and the valve-spindle is several times as much 
as shown in the figure. The lever il, centred at h, is under the 
control of the governor through the rod hi. The eccentric and 
eccentric-strap, with the lever il, form a radial-detachment cut- 
off gear. 



120 VALVE-GEARS FOR STEAM-ENGINES. 

Suppose, first, that the lever hi is thrown so far to the right 
that the toe a does not touch it; then as the centre of the eccen- 
tric describes a circular path around the point O, the point b 
of the line b Ea will move on an arc sensibly parallel with the 
axis XX', and the point a x will describe an oval aia 2 a 3 ; the 
valve meanwhile will remain shut. 

On the other hand, if the lever hi is supposed to be so far 
to the left that the toe a may remain always in contact with its 
curved end, and if by some means it is prevented from rising 
from that surface, then the point a will travel on a circular arc 
nearly coincident with the axis XX', and the point b will describe 
the oval b bib 2 ; such an action is of course impossible when 
the gear is connected up, as the valve is on its seat when the 
point b is on the axis XX' and consequently b cannot rise above 
that axis. 

With the lever hi in the position shown in the figure, the 
toe a describes the oval a\a 2 a z till it comes in contact with the 
curved surface at the end of the lever; and then a slides along 
that surface, while the point b describes the arc bib , and the 
valve is opened as shown by Fig. 2. When the toe comes to 
the edge of the surface /, it slips off and the valve is thrown shut 
by the action of a spring and dash-pot. The toe falls from 
a to Oi, and the point b returns to b on the axis XX'. 

It is evident that this from of valve-gear can give a range of 
cut-off varying from the beginning to the end of the stroke, and 
that the releasing-device does not throw a shock on the governor. 
On the other hand, the sudden opening of the steam-valve when 
the toe a comes in contact with the lever hi throws a shock on 
the valve-gear that might be troublesome at any but the low 
speeds at which pumping-engines are commonly run. 



APPENDIX. 



ANALYTICAL DISCUSSION. 

Crank and Connecting-rod. — The graphical construction for 
the motion of a piston when connected to the crank by a con- 
necting-rod, given on page 2, is customary and convenient. It 
may be desirable to have in addition the following analytical 
discussion of the problem. 

Let the length of the connecting-rod be represented by L } 
the length of the crank by R, and the angle which the crank 
makes with the centre-line XX', by 6; then the displacement 
HA of the cross-head from the beginning of its stroke is 

D = OA-Oc-{HC 2 -C~c 2 )*-, 

D = L + R-R cos 6-(L 2 -R 2 sin 2 6)±; 

P^(x-cos^) + z{x-(i-^^y}. . . (1) 

The principal use of this equation is to study the nature 
of the irregularity introduced by the connecting-rod into the 
motion of the cross-head, and for that purpose it is. convenient 
to expand the expression containing L by the binomial theorem, 



rejecting terms having the higher powers of Lin the denominator; 
whence 

~ „ n, T I / R 2 sin 2 6\ I 
D=R(i—cosd)+L\i-(i ^— J [ 

D = R(l - C05 e) + x^ ( 2 ) 



The ratio of crank to connecting-rod in stationary-engine 
practice varies from i : 5 to 1 : 7 J. In marine engineering the 
ratio 1:4, or even more, sometimes obtains. The maximum 
value of the term containing L occurs at # = 90°; for the ratios 
of crank to connecting-rod just given, the term containing L 
has then the values ~^R, T l jR, %R, respectively. It is appar- 
ent that the difference between the motion of the cross-head 
and piston, and harmonic motion, represented by the equation 

D = R(i-cosd), ...... (3) 

is always notable, and may be large. 

Eccentric and Eccentric-rod. — The displacement of the valve 
is always reckoned from the middle position, and in Fig. 4, 
PL I, is e=ha; it may be calculated as follows: 

e=Oe+Oa-{Eh 2 -Ee 2 )*-, 

.-. e=rcos {90 - (6 + d) }+ 1 -[P-r 2 sin 2 \9o°-(0+d)}f; 

• , a *n ,r ( r 2 cos 2 (d + d))*-} 
.-. e=rsm(d + d)+l[i-\i f \ ]' ' ' ' (4) 

This equation differs from equation (1) only in that the 
eccentric angle and the valve-displacement are reckoned from 
different points. Expanding by the binomial theorem and 



ANALYTICAL DISCUSSION. 123 

rejecting terms containing the higher powers of / in the denom- 
inator gives 

. ,„ ^ r 2 cos 2 (d + d) 



2/ 



(5> 



The length of the eccentric-rod is commonly from 12 to 20 
times the eccentricity; the right-hand terms for such ratio will 
have the values -^r and ^V> respectively, for maxima. It is 
customary to assume the motion of the valve to be harmonic, 
in which case it is represented by the equation 



(6) 



The error of this assumption, though appreciable, is not 
large; moreover the method of setting values of engines pre- 
vents any inconvenience from this source unless the eccentric- 
rods are very short. 

Stephenson Link-motion. — The only satisfactory justification of 
the use of Zeuner's valve diagrams is the analytical discussion 
given by him in his Treatise on Valve-gear. That discussion 
involves the development of a number of long equations, which, 
however, require only a knowledge of simple trigonometry and 
present no great difficulty. 

As presented here the work is perhaps given with undue 
prolixity because it is desired that sufficient intermediate steps 
shall be given to enable any one to read it readily. It will be 
sufficient in any case to follow the . transformations and recognize 
the results. It may be noted that the use of the model described 
on page 64 does not depend on this discussion. 

On Plate XVI the Figures 1 and 2 are drawn to represent 
link-motions with open and with crossed rods. The diagrams 
in thin lines give the positions of the parts when the crank is. 
on the crank-end dead-point; and the diagrams in heavy linesi 
show the positions when the crank has moved through the angle d.. 



124 APPENDIX. 

The eccentricity for each eccentric is r, and the angular 
advance is d. The link-pins are on the link-arc, the length of 
the eccentric-reds is /, and the radius of the link-arc is p which 
may or may not be equal to /. The length of half the link- arc 
is c, and the displacement of the link-block from the middle of 
the link-arc is d. In the discussion it is assumed that the link 
is supported and guided by the link-block, so that the point n 
remains on the line XX' . It is also assumed that the chord 
joining the link-pins is equal to the length of the link-arc between 
those pins, and that in like manner the displacement of the link- 
block from the middle of the link may be measured indifferently 
either on the link-arc or on the chord.. The error of this assump- 
tion may be estimated as follows: A common proportion is 
r=\c=-£ s l i or c = ^/, so that the arc subtends an angle of about 
2o°, and for that angle the arc is 0.3490 of the radius and the 
chord is 0.3473 of the radius, and the error is a little more than 
half of one per cent. 

The distance from the centre of the driver-axle to the middle 
of the valve, in either Fig. 1 or Fig. 2, PI XVI, is 

Ob = Om + mn+nb = Op — mp+mn + nb, ... (7) 

in which the length of the valve-spindle nb may be replaced by 
s, and the value of the other t^rms may be conveniently deter- 
mined as follows : 

First, the term mp is determined by the equation 

mp = mP sin mPp=(c — d) sin a (8) 

Now 

Pjf Op-Op? ■ 

Smft = PF = 20 G>) 

From Fig. 1, PI. XVI, 

Op = Oe + ep=Oe+{EP 2 -(Pp-Ee) 2 }l) . . .(10) 









ANALYTICAL DISCUSSION. 1 25 

and from Fig. 2, 

Op = Oe + ep = Oe+\EP 2 -(Pp + Ee) 2 \K . . (11) 
In either figure 

Oe = r sin (d + d), Ee = r cos (d + d), EP=l, 

and 

Pp = mP cos mPp=(c — d) cos a; 

these values substituted in equations (10) and (n) give 

Op = r sin (6 + d) + {I 2 -[(c-d) cosa^rcos (d + d)] 2 \$; (12) 

the upper sign being taken for open and the lower sign for crossed 
rods. Expanding the term with a fractional exponent by the 
binomial theorem, and rejecting terms with the higher powers of 
I in the denominator, gives 

, (c — d) 2 cos 2 a 
Op=r sin (6 + d)+l-- ^ 

(c - d)r co s (d + §) cos a r^cos 2 (d + d) 



I 2/ 

Now the terms containing cos a in the numerator have / in the- 
denominator, and are comparatively small, while a is not more 
than 30 , for which the cosine is 0.866; consequently we may 
replace unity for cos a without much error. With that change 
and some expansion, 

t. C HJL 

~2l + l 2 

(c - d)r cos (d + d) r 2 cos 2 (d + 6) 



I 2/ 



(13) 



Similarly Fig. i and Fig. 2 give respectively equations (14) and 
<i5) = 

Op' = e'p' -Oe?=\ WP' 2 - (P'p f - E'e') 2 )*-Oe'\ . (14) 

Op' = e'p' -Oe' = {WF 2 -(P'p' +E'e') 2 \*-Oe'. . (15) 

In either figure 

Oe' = r sin (6 - d), E'e' = r cos (6 - d), E'P' =1, 
and 

P'p' = mP' cos mP'f = (c+d) cos a ; 

these terms substituted in equations (14) and (15) give 

Op'= -rsin (d-d) + {l 2 -[{c+d) cosaTrcos (d-d)] 2 ]*; (16) 

the upper sign being taken for open and the lower for crossed 
rods. As in the previous work, cos a may be replaced' by 
unity; expanding by the binomial theorem, and rejecting terms 
with the higher powers of / in the denominator, gives 

(c+d) 2 
Of=-rsm (d-d)+l-^~ 

(c+d)r cos (d-d) r 2 cos 2 (d-d) 
± I 2l '' 

c 2 cd d 2 

(c + d)r cos (d-d) r 2 cos 2 (6 -d) 
± I 2/ 

Substituting in equation (9) the values for Op and Of, 



(17) 



ANALYTICAL DISCUSSION. 127 



r sin (0 + d) +r sin (6 - d) 2cd 
sin a = 1- — ; 

2C 2Cl 



(c - d)r cos (0 + d)-(c+d)r cos ( 

± 2C/ 



r 2 cos 2 (0 + a)-r 2 cos 2 (0-a) 
4 c/ ' 



sin a =— cos d sin 0^-; sin £ sin 0=F — ; cos £ cos 



+ y-^[cos 2 (0 + £)-cos 2 (d-d)]. (18) 



To obtain an expression for the term mn in equation (7) 
consider Fig. 3, PL XVI, where Puq is half the link and n T is 
the diameter of the arc Pn , while On corresponds to the line 
OnX f of Fig. 1. If the half -chords Pm and ni are drawn, 
it may be admitted that mn is nearly equal to m i, so that 
approximately 

mn=mon —ino. 

But noting that the diameter n T is divided into segments both 
by Pmo and by ni, and that the smaller segments are very small 
compared with the larger segments, we may write 



mn=—-7f--7^= (nearly). . . (19) 

moT %T 2p 2p v J v y 



Substituting in equation (7) the values of the several terms, 



c 2 cd d 2 

Ob = r sin d cos d + r cos d sin 6+1 — r + -j r 

2I I 2/ 



± — (cos u cos o — smu sin 0) — j 

{r r dr 

-cos d sin 6 +~ —sin sin 6 + — cos 5 cos 
c / c/ 

^ ) c 2 d 2 
8)] [ + +s', 

J J 2p 2p 



+ y--^[cos 2 (0 + d)-cos : 



c — d . d 

Ob = r[sm d ± — t— cos d ± (c — d)— f cos d] cos d 

* c ~d ■ * c ~d * c—d . „ . . 
+r[cos ^T— ;— sin <? cos o±— l— sin d] sin 



— ^ { 2c cos 2 (<?+ 0) - (c-d)[cos 2 (# + £)- cos 2 (0-d)]} 

—c 2 p + 2cdp — d 2 p — 2(c — d)dp + c 2 l — d 2 l 
+• ^V +l+s\ 

2Lp 

/ c 2 — d 2 \ d 

.♦. Ob = rl sin <?± — ^ — cos d) cos d+r — cos £sin0 



Uc+d) cos 2 (d+6) + (c-d) cos 2 (d-d)] 

+ (c 2 ~d 2 )^+l+s (20) 

The third term has its greatest value when d is equal to c % 
and it is then equal to 



AN 'A LYTIC A L DISCUSSION. 129 

which is the term that appears in equation (5) for the plain 
slide-valve. In the discussion of the plain slide-valve this term 
was neglected, and consequently it may be neglected here with 
equal propriety. Equation (20) may therefore be written 

/ c 2 -d 2 \ d 

Ob = r[ sin d± j— cos d I cos d + r— cos d sin d 






+ ( C 2 -d 2 )^ + l + S. 21) 



If the engine is on the crank-end dead-point, then 6 is zero; 
and it is 180 at the head-end dead-point. These special values 
of the crank-angle give 

Ob f =r{sin d± C ^^ cos d)+(c 2 -d 2 ) l ^+l+s; . (22) 



Ob 1 



--rUmd± { cosd)+(c 2 -d 2 )-^+l+s. (23) 



The mid-position of the valve should be midway between 
V and b", Figs. 1 and 2, PL XVI; half the sum of Ob' and Ob" is 

0tf= o^o^ (c2 _^ +/+j . _ _ (24) 

in which the only variable is the term containing p, the radius 
of curvature of the link-arc. If p be made equal to I, then this 
term disappears, leaving 

Oo=l+s (25) 

With equal laps, the necessary and sufficient condition for 
equal leads, at all grades, is that the radius 0} the link-arc shall 
be equal to the length of the eccentric-rod., 



130 APPENDIX. 

Applying this condition to equation (21) gives 

( C 2—(P \ d 

sin d± — 7— cos d J cos d + r- cos d sin 6+l+s. (26) 

The displacement of the valve from mid-position is 

e = Ob-Oo; 

(fi—d 2 \ d 

sind± — j— cos dj cos 6 + r- cos d sin 6. . (27) 

General Equation for Valve-motion. — Equation (6), page 123, 
gives for the displacement of a plain slide-valve moved by an 
eccentric 

e = rsm(d+d)', 

expanding the parenthesis, 

e^cosdsintf+fsin^cosfl; .... (28) 

which may be written 

e=Acosd+Bsm6, (29) 

since r and d are constant for a given slide-valve gear. 

It has been shown by the aid of Fig. 7, PI. II, that the 
motion of a plain slide-valve may be represented by a valve- 
circle, and a comparison of that figure with equation (29) will 
show that the constants in the equation are the coordinates of 
the end P of the diameter of the valve-circle. Thus 

Oq=r sin d= A; (31) 

Pq=r cos d=B (32) 



J 



ANALYTICAL DISCUSSION. 13 1 

It may be concluded that any valve which has its displace- 
ment represented by an equation of the same form as equation 
(29) has a harmonic motion and may have its motion repre- 
sented by a valve-circle. 

Zeuner's Diagram. — A comparison of equation (27) with 

equation (29) shows that a valve controlled by a Stephenson 

link-motion has a harmonic motion, and that its displacements 

from mid-position, at any grade of the link, may be represented 

by a valve-circle, having for the coordinates of the end of the 

diameter 

/ c 2 -d 2 \ 
A=r[smd±—-j—cosd\-, (33) 

d 
B = r-cosd (34) 

At full-gear d=c, which applied to equations (33) and (34) 
will reduce them to equations (31) and (32). Thus the valve- 
diagram for a link-motion at full gear is identical with the dia- 
gram for a plain slide-valve under the control of an eccentric 
having the same eccentricity and angular advance as one of 
the eccentrics of the link-motion; which coincides with our 
conceptions of the link-motion, derived from the drawings on 
Plates XIII and XIV. 

In Fig. 4, PI. XVI, and Fig. 1, PI. XVII, Oq and qP are 
made equal to the coordinates of the end of the valve-circle 
diameter at full-gear, when d=c; i.e., 

Oq=r sin d = A, qP = r cos d=B. 

At mid-gear d becomes zero, and the coordinates of the end 
of the diameter of the valve-circle become 



Ao=rsm <?±ycos d; (35) 

Bo=o (36) 



The upper sign is taken for open rods, and the lower sign for 
crossed rods. Fig. 4, PI. XVI, corresponds with the first case, 
and Fig. 1, PI. XVII, with the second case. The ends of the 
diameter of valve-circles for intermediate grades of the link 
may be found by assuming values for d and calculating the co- 
ordinates by aid of equations (33) and (34), if desired; but an 
inspection of those equations shows that they give the coordi- 
nates of a parabola having its vertex on the axis XX'. Two 
points, P and P , are already located and an arc of the parab- 
ola may be passed through them by the ordinary geometrical 
construction; or, since the arc is quite flat, there may be sub- 
stituted for it the arc of a circle having its centre on the axis 
XX'. The centres of the valve-circles have for their coordi- 
nates \A and \B, and consequently lie on another parabola 
with its vertex on XX' \ an arc of a circle centred on XX' may 
be substituted for the arc of this parabola, and will be more con- 
venient to draw since its radius is half the radius of the circular 
arc substituted for the parabola through P and Pq. 

Fig. 4, PL XVI, and Fig. 1, PI. XVII, exhibit the variation 
of lead which was pointed out in Figs. 1 and 2, PI. XV. The 
same thing is evident from an inspection of equation (33), tak- 
ing the upper sign for open and the lower sign for crossed rods. 
For convenience the fact is stated as follows : 

A Stephenson link-motion with open rods gives increasing 
lead from full-gear toward mid-gear; with crossed rods it gives 
decreasing lead from full-gear toward mid-gear. 

Valve-circles showing the motion of teh valve at intermedi- 
ate grades of the link are drawn at OPi and OP 2 , on Fig. 4, PL 
XVI, and on Fig. 1, PL XVII. On both figures the lap-circles 
are nn'n", showing cut-off at the crank-positions OR, OR\, 
OR 2 , and OR ; neglecting the influence of the connecting-rod, 
the corresponding piston-displacements are xa, xa\, xa 2 , and 
xa . An inspection of the figure will show that the lead angle 
increases as the cut-off is shortened, accompanied by an earlier 



ANALYTICAL DISCUSSION. 133 

admission. If an exhaust-lap circle were drawn, it would show 
that an early cut-off is accompanied by an early release and a 
large compression. A comparison of these diagrams with the 
valve-diagrams shown by Fig. 2, PL X, and Fig. 1, PI. XII, will 
show that a Stephenson link-motion is equivalent to a shifting 
eccentric with variable lead. 

Gooch Link-motion. — Making use of the same notation as 
in the .analytical discussion of the Stephenson link, let e be the 
eccentricity, and d the angular advance for each eccentric; let 
c be the half-length of the link, and d the displacement of the 
link-block from the middle of the link; let I be the length of 
the eccentric-rod, the link-pins being assumed to be on the link- 
arc; let h be the length of the radius-rod, and 5 the length of 
the valve-spindle. 

Assume that the link is so suspended that m, the middle 
point of the chord, shall remain on the central line XX', and 
that the length of the link is sensibly the same whether meas- 
ured on the chord or on the arc. Assume also that the rods 
are open. 

In Fig. 2, PI. XVIII, the diagram in fine lines represents the 
link-motion when the crank is on a dead-point; and the diagram 
in heavy lines represents it when the crank has moved from 
Co to C through the angle d. 

The distance from the origin O to the middle of the valve b 
is 

Ob = Op-pk-kq + qS + Sb (37) 

The term pk is determined by the equation 

pk = KP sin pPK=(c-d) sin a (38) 



Now 



pi/ Op-Op , v 

Sm « = ^7- \ c (39) 



134 APPENDIX. 

But 

Op= Oe +ep = Oe +{EP 2 -(Pp-Ee) 2 \*; . . (40) 

Op'=-Oe' + e'p=-Oe'+{l?P' 2 -(P'p-E , e')2\i-, . (41) 
in which 

EP = E'P'=l, Pp = P'f=c cos a; 

Oe = r sin (d + d), Oe' = r sin (6 - d) ; 
Ee = r cos (d + d), Ee' = r cos (d — 0). 

Substituting these values in equations (40) and (41) gives 

Op = r sin (6 +d)+ \l 2 -[c cos a-r cos {6 +^)] 2 |i . (42) 

0^=-/-sin(^-a)+{/ 2 -[ccosa:-ycos(^-^)] 2 ^. . (43) 

A comparison of equations (42) and (43) with equations (12) 
and (16) shows that they differ in that the coefficient of cos a 
does not contain d, and that only the upper sign of the double 
sign appears before the last term in the bracket ; this last, because 
the discussion applies only to open rods. Consequently the - 
value of sin a may be obtained from equation (18) by omit- 
ting terms containing d, and using only the upper sign of the 
double signs; hence 






--4[cos 2 (0 + ,5)-cos2(0-,S)]. (44) 

4c/ 

Expanding by the binomial theorem the term in equation 
(42) which has a fractional exponent, and rejecting terms with 



ANALYTICAL DISCUSSION. 1 35 

higher powers of / in the denominator, and at the same time 

substituting unity for cos a, will give 

Op-rsin(e + S,+l- C U^cos(e + S,- r2cos2 f + S) . (45) 

2b I 2L 



The first two terms of the equation (37) are now determined; 
the others are 

Sb=s, 



and 



qS={l l 2 -d 2 \^=h~ (nearly), 



**-5rr3- 1 < neatl y ) - 



To obtain the last equation, it may be admitted that qk (Fig. 2, 
PL XVIII) is nearly equal to QK, which is nearly equal to tm. 
Now Pm is half of a chord bisected by a diameter, of which one 
segment is nm and the other is 2h—mn; consequently 

Pm 2 = nm{2l\ — mn) ; 



.*. mn = -j- (nearly); 



and in like manner 



nt=—r- (nearly). 

tm = kq=—j r- (nearly). 

* 2/1 2/1 v ■" 



I36 APPENDIX. 

Substituting the values of the several terms in equation (37), 

. ,„ .v , c 2 cr cos (d + d) r 2 cos 2 (d + d) 
0& = rsin(tf + d)+/-^ + j ~ 



—(c—d) j — sin 6 cos d— j sin d sin d 

r 2 ) c 2 d 2 d 2 

+ _ [cos2( ,_, ) _ cos2((?+ , )] |__ + _ + ; 1 _ i _ + ,. 



Ob=r sin 6 cos d+r cos d sind-\-j cos cos d 



—r sin # sin d — r sin cos £+y sin 6 sin d 



dr dr c 2 c 2 

+ — sin 6 cos £ — -7" sin sin £ + / : j- +/1+5 

c j 2/ 2^1 



^cos 2 (0 + £)-^cos 2 (#-<5) + ^ COS 2 (0 + 0) 

_ cos2 (,_,)__ cos2( , + , ); 

I sin £+y-cos 5 j cos d+— (cos £— y-sin <5] sin 



Ob=r sin £ + y cos c 



c 2 e 2 

+/+/l+5 -^-27T 



— ^[(c+d)cos 2 (0 + <5) + (c-</)cos 2 (0-<?)]. . . . (46) 

The last term is identical with the term dropped from equa- 
tion (20), and it may be neglected here as well. 



ANALYTICAL DISCUSSION. 



At the crank-end dead-point 6 is zero, and it is 180 at the 
head-end dead-point. The corresponding values for Ob are 

/ c \ c 2 c 2 

OV =rl sin d+j cos d )+l+h +s-—j — r5 • (47) 

(c \ c 2 c 2 

sin d+j cos d \+l+h +s — 7 — p . (48) 

Hence the distance from the origin O to the middle of the valve, 
when in mid-position, is (Fig. 2, PL XVIII) 

Oo=%(Ob x +Ob 2 )=l+h+s-j l ~. . . . (49) 

The displacement of the valve from mid-position at any 
crank-angle is obtained by subtracting equation (49) from equa- 
tion (46), member from member, giving 

e=rl sin d+j cos d) cos d+— (cos d— j sin djsinfl. (50) 

Thus far in this discussion attention has been given to the 
case of open rods only; were the same method to be carried 
through for crossed rods, using a figure similar to Fig. 2, PL 
XVIII, a similar equation would be found for the valve-dis- 
placement, except that the quantities c and d would be affected 
by a negative sign. 

Zeuner's Diagram. — A comparison of equation (50) with 
equation (29) shows that a valve controlled by a Gooch link- 
motion has a harmonic motion, and that its displacement from 
mid-position, at any grade of the link, may be represented by 
a valve-circle. Taking account of the observation at the end 
of the previous paragraph, with regard to crossed rods, the co- 
ordinates of the end of the diameter of the valve-circle may be 
written 



■.« 



138 APPENDIX. 

A=rl sin d±ycosd); (51) 

B = -(cosdTjsmdj; (52) 

the upper sign being used with open and the lower with crossed 
rods. 

The expression for A, the abscissa of the end of the diam- 
eter of the valve-circle, is the same for all grades of the link; 
which agrees with the statement on page 53 that the lead is 
constant when the radius of the link-arc is equal to the length 
of the radius-rod. It is apparent, therefore, that a Gooch link- 
motion is equivalent to a shifting eccentric with constant lead. 
Fig. 3, PI. XVII, gives the valve-circles for full-gear, mid-gear, 
and for two intermediate gears; and shows the variation of 
cut-off from full-gear to mid-gear. As was found to be the 
case with the shifting eccentric, constant lead is found to be 
accompanied by an earlier admission from full-gear toward 
mid-gear, though the change is not so marked as it is with an 
increasing lead. 

It must be noted that the Gooch link-motion at full-gear 
does not give the valve the motion that it would have if the con- 
nection were made by an eccentric-rod to the head of the valve- 
spindle. In this respect the action of the Gooch link-motion 
differs from the Stephenson link-motion, which at full-gear 
acts like a plain slide-valve gear. The diameter of the valve- 
circle is, at full-gear, 

/ c 2 c 

(A 2 + B 2 )* = r ( sin 2 d+j 2 cos 2 d±2j sin d cos d 

c 2 c \i 

+cos 2 d+-» sin 2 ^27 sin d cos d J 

■ 2 \i 



'( I+ £) 



M 



ANALYTICAL DISCUSSION. 139 

which for the ordinary proportions of the link-motion is a trifle 
longer than r. Consequently the full-gear action of a Gooch 
link-motion with open rods is equivalent to that of a plain slide- 
valve gear with a little greater angular advance; with crossed 
rods it is equivalent to the action of such a gear with a little 
less angular advance. The difference in each case, though not 
large, is appreciable. 

Walschaert Gear. — The motion of a valve controlled by 
this gear can be represented in a general way by Zeuner's dia- 
grams, but the discrepancy between the results from such dia- 
gram and the actual valve-motion is too large to allow us to 
use the diagrams even for a preliminary design. The general 
conception, however, is a very important matter. 

The displacement from mid-position of a valve moved by 
an eccentric is 

e=rsin(6 + d). 

Now the motion derived from the cross-head is equivalent to 
that from an eccentric having 90 angular advance, provided 
the cross-head motion is assumed to be harmonic. Conse- 
quently the valve derives a displacement from this source of 

ei=ri sin (d + go°) = ri cos 6 (53) 

From the proportions of the combining-lever and the length 
R of the crank, we have 



ri = 



-**• 



The displacement of the valve from the influence of the 
eccentric OE is 

e 2 =r 2 sin (0+o o )=r2sin0, (54) 

in which 



The entire displacement e of the valve at any crank-angle 
is the sum of the displacements of the two independent sources. 

.*. e = ei + e 2 = fi cos0+r 2 sin0; . . . (55) 

and since r\ and r 2 are constant for any grade of the link, equa- 
tion (55) is a special case of equation (29), r\ and r 2 being the 
coordinates of the diameter of a valve-circle for that grade of 
the gear. 

In Fig. 1, Plate XXI, the valve-circle OP is drawn with a 
diameter ri and represents the mid -gear action of the valve. 
The circles Op, Op\, and Op 2 represent the motions derived 
from the eccentric OE x at full-gear and at two intermediate 
gears. The circles OP, OP\, and OP 2 represent the actual dis- 
placements of the valve, derived from both sources. It is evi- 
dent that 

OP=\OP 2 + Op 2 \\ 

and that OP\ and OP 2 may be obtained in a similar manner. 
A comparison of Fig. 1, PI. XXI, with Fig. 3, PI. XVII, shows 
that the action of the Walschaert gear is equivalent to that of 
the Gooch link-motion. To aid in this comparison, the dimen- 
sions OPo and P P were transferred from Fig. 3, PI. XVII, to 
Fig. 1, PI. XXI, and consequently the diagrams are identical. 



INDEX. 



Admission, 5 

Allen valve, 30 

Analytical discussion, 121 

Angular advance, 4, 24 

Area of steam-pipe and steam-ports, 36 

Auxiliary valve-circle, 98 

Balanced valves, 31 
Bell-crank lever, 21 
Brown engine gear, 109 

Clearance, 13 

Compression, 13 

Corliss valve-gear, 112 

Crank and connecting-rod, 121 

Cut-off, 5 

" equalization of, 18, 25 

Cut-off valve on back of main valve, 97 
" " in separate chest, 92 

" " with constant travel, 105 

" " with shifting eccentric, 95 

Dead-centre, to set engine on, 32 
Designing Meyer valve, 100 

" link-motions, 59 
Diagram, elliptical, 5 

" sinusoidal, 7 

" Zeuner's, 8 
Double-ported valve, 30 
Double valves, 92 

" " auxiliary circle, 98 

Drop cut-off valve-gears, 109 



Eccentric and eccentric-rod, 122 
Equalization of cut-off, 18, 24 
Events of the stroke, 5 
Expansion and compression, 13 

Gaskill valve-gear, 119 
General equation, 130 
Gooch link-motion, 52, 133 

Hackworth valve-gear, 88 

Joy valve-gear, 88 

Lap, steam and exhaust, 4 

Lead, 4, 14 

Lead-angle, 14 

Link-arc, radius of, 50, 53, 58 

Link-motion, 47 

' ' adjusting cut-off, 62 

" analytical discussion, 123, 

133 
" designing, 59 

' ' for locomotives, 63 

" for marine engines, 56 

" Gooch, 52, 133 

" location of reverse-shaft, 

73 
' ' location of rocker, 72, 73 

" " " saddle-pin, 72 

" modifications, 57 

" open and crossed rods, 

53.49 

141 



I 4 2 



Link-motion, port-opening, 74 

" saddle-pin, 57 

" skeleton model, 64 

slip, 74 

" Stephenson, 47, 54, 123 

" to set, 76 

" Zeuner's diagram, 51 

Link-pins, 57 
Loose eccentric, 40 

Marine link-motions, 56, 60 
Marshall valve-gear, 86 
Meyer valve-gear, 99 

' ' cut-off at inner edge, 

102 
" designing, 100 

" " for reversing en- 

gines, 103 
Model for link-motion, 64 

" " " applications, 77 

Piston-valve, 28 
Port-opening, 74 
Ports, 3 

' ' area of, 36 
Putnam valve-gear, 117 

Radial valve-gears, 84 

Radius of link-arc, 50, 53 

Reduction of slip of link-motion, 61 

Release, 5 

Reverse-shaft for link-motion, 58, 73 

Rocker, 21 

' ' equalization of cut-off by, 24 
' ' location for link-motion, 72 

Saddle-pin, 57 
Shaft-governor, 41 
Shifting-eccentric, constant lead, 46 
variable lead, 43 
Sinusoidal diagram, 7 
Skeleton model for link-motion, 64 



Skeleton applications, 77 
Slide-valve, 1, 3 

" problems, 14 
" to lay out, 20 
Slip of link-motion, 74 
" reduction of, 61 
Steam-pipe, area of, 36 
Stephenson link-motion, 47, 54, 123 
Stroke, events of, 5 

To set a double valve, 107 
" " link-motion, 76 
" " slide-valve, 32 
" " an engine on a dead-point, 32 
Trick valve, 30 

Valve, Allen or Trick, 30 
" balanced, 31 
" double-ported, 30 
" piston, 28 
Valve-circle, auxiliary, 98 
Valve-ellipse, 5 

Valve-gear, Brown engine, 109 
" cam, no 

" Corliss, 112 

" double, 92 

" drop cut-off, 109 

" Gaskill, 119 

" Hackworth, 88 

" Joy, 88 

" Marshall, 86 

" Meyer, 99 

" Putnam, 117 

" radial, 84 

" Walschaert, 85 

Valve-setting, for double valves, 107 
' ' for link-motions, 76 

' ' for slide-valve, 32 

Walschaert gear, 85, 139 

Zeuner's diagram, 8, 51, 131, 137 



14: 

Liri 



Lii 
Lo 



M; 
M; 



Pc 
P( 



Plate II. 





g o •^<™-^ ~ 



Plate II, 




/" - 




^ 


:■ 













S o •-<-=■- c 



Plate IIL 




Plate IV 




Plate V, 




Plate VI. 




.- 


- 


y ^°° 




\ 


1 /° 






r 


/ 


■ — i 
< 


X 


,---'' 



PLATE XV. 



Plate XVI. 



!p $ o v. X 




i 



-i.l 



Plate XX. 




Plate XXa. 





Fig. 7 





Plate XXI. 




1 II 


IV // 


1/ 


II 


}(^jK \\ 




X 







Plate XXI. 




\ \ i \ \ ?£ 


w ^ / / A/ 




\ 1 \ \ \ J 


^^' //// 




\ \ \ \ i i 


H tj 1 1 




\\ ' \ fa 

\ , v & i ! 
v co / i [ 

ii 

1/ 

i 


"« / // 






CN /j 

bb '[ 
£ 'j 




oc/ 


(O^M 


1 


\ )'] 


r r* 


2^ 


o / J 


li/'i \ 


\ v\ 


/3sf=fu^7r 




X v a \j^>^ 


of / J . - 


| /Ul \ I \ 

3J// \ \ \\ 




^~~"^£sL x 


l/^C 


4^/ / 




"^--— 





Plate XXIII. 





Plate XXIV. 



Plate XXI V.I 




Plate XXV. 




Fig. 3 



~n~ 



lid 



-U r % 



f^j 




V. 



Elate XXVII. 



f—^ ) {% /7~ r f- 



Fig. 2 Q 




I 



Plate XXXIL 





! 



SHORT-TITLE CATALOGUE 

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Winton's Microscopy of Vegetable Foods 8vo, 

Wulling's Elementary Course in Inorganic, Pharmaceutical, and Medical 

Chemistry i2mo, 

5 



3 


00 


2 


50 


I 


50 


3 


00 


3 


00 


4 


00 


5 


00 


i 


50 


4 


oo 


4 


00 


2 


00 



7 So 

2 OO. 



CIVIL ENGINEERING. 

BRIDGES AND ROOFS. HYDRAULICS. MATERIALS OF ENGINEERING. 
RAILWAY ENGINEERING. 

Baker's Engineers' Surveying Instruments i2mo, 3 00 

Bixby's Graphical Computing Table Paper 19^X24} inches. 25 

** Burr's Ancient and Modern Engineering and the Isthmian Canal. (Postage, 

27 cents additional.) 8vo, 3 50 

Comstock's Field Astronomy for Engineers 8vo, 2 50 

Davis's Elevation and Stadia Tables 8vo, 1 00 

Elliott's Engineering for Land Drainage i2mo, 1 50 

Practical Farm Drainage nmo, 1 00 

*Fiebeger's Treatise on Civil Engineering 8vo, 5 00 

Folwell's Sewerage. (Designing and Maintenance.) 8vo, 3 00 

Freitag's Architectural Engineering. 2d Edition, Rewritten 8vo, 3 50 

French and Isres's Stereotomy 8vo, 2 50 

Goodhue's Municipal Improvements i2mo, 1 75 

Goodrich's Economic Disposal of Towns' Refuse 8vo, 3 50 

Gore's Elements of Geodesy 8vo, 2 50 

Hayford's Text-book of Geodetic Astronomy 8vo, 3 00 

Hering's Ready Reference Tables (Conversion Factors) i6mo, morocco, 2 50 

Howe's Retaining Walls for Earth i2mo, 1 25 

Johnson's (J. B.) Theory and Practice of Surveying Small 8vo, 4 00 

Johnson's (L. J.) Statics by Algebraic and Graphic Methods 8vo, 2 00 

Laplace's Philosophical Essay on Probabilities. (Truscoit and Emory.), nmo, 2 00 

Mahan's Treatise on Civil Engineering. (1873.) (Wood.), 8vo, 5 00 

* Descriptive Geometry 8vo, 1 50 

Merriman's Elements of Precise Surveying and Geodesy Svc s 2 50 

Merriman and Brooks's Handbook for Surveyors i6mo, moroc. - 00 

Nugent's Plane Surveying 8vo, 3 Sc 

Ogden's Sewer Design i2mo, 2 00 

Patton's Treatise on Civil Engineering 8vo half leather, 7 50 

Reed's Topographical Drawing and Sketching 4to, 5 00 

Rideal's Sewage and the Bacterial Purification of Sewage 8vo, 3 50 

Siebert and Biggin's Modern Stone-cutting and Masonry 8vo, 1 50 

Smith's Manual of Topographical Drawing. (McMillan.) 8vo, 2 50 

Sondericker's Graphic Statics, with Applications to Trusses, Beams, and Arches. 

8vo, 2 00 

Taylor and Thompson's Treatise on Concrete, Plain and Reinforced 8vo, 5 00 

* Trautwine's Civil Engineer's Pocket-book i6mo, morocco, 5 00 

Wait's Engineering and Architectural Jurisprudence 8vo, 6 00 

Sheep, 6 50 
Law of Operations Preliminary to Construction in Engineering and Archi- 
tecture 8v °> S 00 

Sheep, 5 50 

Law of Contracts 8vo » 3 00 

Warren's Stereotomy — Problems in Stone-cutting 8vo, 2 50 

Webb's Problems in the Use and Adjustment of Engineering Instruments. 

i6mo, morocco, 1 25 

Wilson's Topographic Surveying 8vo, 3 50 



BRIDGES AND ROOFS. 

Boiler's Practical Treatise on the Construction of Iron Highway Bridges. .8vo, 

* Thames River Bridge 4to, paper, 

Burr's Course on the Stresses in Bridges and Roof Trusses, Arched Ribs, and 
Suspension Bridges 8vo, 



Burr and Falk's Influence Lines for Bridge and Roof Computations. . . .8vo, 3 «» 

Design and Construction of Metallic Bridges 8vo, 5 00 

Du Bois's Mechanics of Engineering. Vol. II Small 4to, 10 00 

Foster's Treatise on Wooden Trestle Bridges 4to, 5 00 

Fowler's Ordinary Foundations 8vo, 3 50 

Greene's Roof Trusses 8vo, 1 25 

Bridge Trusses 8vo, 2 50 

Arches in Wood, Iron, and Stone 8vo, 2 50 

Howe's Treatise on Arches 8vo, 4 00 

Design of Simple Roof-trusses in Wood and Steel 8vo, 2 00 

Johnson, Bryan, and Turneaure's Theory and Practice in the Designing of 

Modern Framed Structures Small 4to, 10 00 

Merriman and Jacoby's Text-book on Roofs and Bridges: 

Part I. Stresses in Simple Trusses. . ." 8vo, 2 50 

Part II. Graphic Statics 8vo, 2 50 

Part III. Bridge Design 8vo, 2 50 

Part IV. Higher Structures 8vo, 2 50 

Morison's Memphis Bridge 4to, 10 00 

Waddell's De Pontibus, a Pocket-book for Bridge Engineers. . i6mo, morocco, 2 00 

Specifications for Steel Bridges i2mo, 1 25 

Wright's Designing of Draw-spans. Two parts in one volume 8vo, 3 50 



HYDRAULICS. 

Bazin's Experiments upon the Contraction of the Liquid Vein Issuing from 

an Orifice. (Trautwine.) 8vo, 2 00 

Bovey's Treatise on Hydraulics 8vo, 5 00 

Church's Mechanics of Engineering 8vo, 6 00 

Diagrams of Mean Velocity of Water in Open Channels paper, 1 50 

Hydraulic Motors 8vo, 2 00 

Coffin's Graphical Solution of Hydraulic Problems i6mo, morocco, 2 50 

Flather's Dynamometers, and the Measurement of Power i2mo, 3 00 

Folwell's Water-supply Engineering 8vo, 4 00 

Frizell's Water-power 8vo, 5 00 

Fuertes's Water and Public Health i2mo, 1 50 

Water-filtration Works i2mo, 2 50 

Ganguillet and Kutter's General Formula for the Uniform Flow of Water in 

Rivers and Other Channels. (Hering and Trautwine.) 8vo, 4 00 

Hazen's Filtration of Public Water-supply 8vo, 3 oo 

Hazlehurst's Towers and Tanks for Water- works 8vo, 2 50 

HerscheFs 115 Experiments on the Carrying Capacity of Large, Riveted, Metal 

Conduits 8vo, 2 00 

Mason's Water-supply. (Considered Principally from a Sanitary Standpoint.) 

8vo, 4 00 

Merriman's Treatise on Hydraulics 8vo, 5 00 

* Michie's Elements of Analytical Mechanics 8vo, 4 00 

Schuyler's Reservoirs for Irrigation, Water-power, and Domestic Water- 
supply Large 8vo, 5 00 

** Thomas and Watt's Improvement of Rivers. (Post., 44c. additional.). 4to, 6 00 

Turneaure and Russell's Public Water-supplies 8vo, 5 00 

Wegmann's Design and Construction of Dams 4x0, 5 00 

Water-supply of the City of New York from 1658 to 1895 4to, 10 00 

Williams and Hazen's Hydraulic Tables 8vo, 1 50 

Wilson's Irrigation Engineering Small 8vo, 4 00 

Wolff's Windmill as a Prime Mover 8vo, 3 00 

Wood's Turbines 8vo, 2 50 

Elements of Analytical Mechanics 8vo, 3 00 

7 



MATERIALS OF ENGINEERING. 

Baker's Treatise on Masonry Construction 8vo, 5 00 

Roads and Pavements 8vo, 5 00 

Black's United States Public Works Oblong 4to, 5 00 

* Bovey's Strength of Materials and Theory of Structures 8vo, 7 50 

Burr's Elasticity and Resistance of the Materials of Engineering 8vo, 7 50 

Byrne's Highway Construction 8vo, 5 00 

Inspection of the Materials and Workmanship Employed in Construction. 

i6mo, 3 00 

Church's Mechanics of Engineering 8vo, 6 00 

Du Bois's Mechanics of Engineering. Vol. I Small 4to, 7 50 

*Eckel's Cements, Limes, and Plasters 8vo, 6 00 

Johnson's Materials of Construction Large 8vo, 6 00 

Fowler's Ordinary Foundations 8vo, 3 50 

* Greene's Structural Mechanics 8vo, 2 50 

Keep's Cast Iron 8vo, 2 50 

Lanza's Applied Mechanics 8vo, 7 50 

Marten's Handbook on Testing Materials. (Henning.) 2 vols 8vo, 7 50 

Maurer's Technical Mechanics 8vo, 4 00 

Merrill's Stones for Building and Decoration 8vo, 5 00 

-Merriman's Mechanics of Materials 8vo, 5 00 

Strength of Materials nmo, 1 00 

Metcalf 's Steel. A Manual for Steel-users i2mo, 2 00 

Patton's Practical Treatise on Foundations 8vo, 5 00 

Richardson's Modern Asphalt Pavements 8vo, 3 00 

Richey's Handbook for Superintendents of Construction i6mo, mor., 4 00 

Rockwell's Roads and Pavements in France i2mo, 1 25 

Sabin's Industrial and Artistic Technology of Paints and Varnish 8vo, 3 00 

Smith's Materials of Machines i2mo, 1 00 

Snow's Principal Species of Wood 8vo, 3 50 

Spalding's Hydraulic Cement i2mo, 2 00 

Text-book on Roads and Pavements nmo, 2 00 

Taylor and Thompson's Treatise on Concrete, Plain and Reinforced 8vo, 5 00 

Thurston's Materials of Engineering. 3 Parts 8vo, 8 00 

Parti. Non-metallic Materials of Engineering and Metallurgy 8vo, 2 00 

Part II. Iron and Steel. 8vo, 3 50 

Part III. A Treatise on Brasses, Bronzes, and Other Alloys and their 

Constituents 8vo, 2 50 

Thurston's Text-book of the Materials of Construction 8vo, 5 00 

Tillson's Street Pavements and Paving Materials 8vo, 4 00 

Waddell's De Pontibus. (A Pocket-book for Bridge Engineers.). . i6mo, mor., 2 00 

Specifications for Steel Bridges nmo, 1 25 

Wood's (De V.) Treatise on the Resistance of Materials, and an Appendix on 

the Preservation of Timber 8vo, 2 00 

Wood's (De V.) Elements of Analytical Mechanics 8vo, 3 00 

Wood's (M. P.) Rustless Coatings: Corrosion and Electrolysis of Iron and 

Steel 8vo, 4 00 



RAILWAY ENGINEERING. 

Andrew's Handbook for Street Railway Engineers 3x5 inches, morocco, 1 25 

Berg's Buildings and Structures of American Railroads 4to, 5 00 

Brook's Handbook of Street Railroad Location i6mo, morocco, 1 50 

Butt's Civil Engineer's Field-book i6mo, morocco, 2 50 

Crandall's Transition Curve i6mo, morocco, I 50 

Railway and Other Earthwork Tables 8vo, 1 50 

Dawson's "Engineering" and Electric Traction Pocket-book. . i6mo, morocco, 5 00 



Dredge's History of the Pennsylvania Railroad: (1879) Paper 

* Drinker's Tunnelling, Explosive Compounds, and Rock Drills. 4to, half r 

Fisher's Table of Cubic Yards Cardboard, 

Godwin's Railroad Engineers' Field-book and Explorers' Guide. . .i6mo, 1 

Howard's Transition Curve Field-book i6mo, morocco, 

Hudson's Tables for Calculating the Cubic Contents of Excavations and Em- 
bankments 8vo, 

Molitor and Beard's Manual for Resident Engineers i6mo, 

Nagle's Field Manual for Railroad Engineers i6mo, morocco : 

Philbrick's Field Manual for Engineers. . . t i6mo, morocco, 

Searles's Field Engineering i6mo, morocco 

Railroad Spiral i6mo, morocco, 

Taylor's Prismoidal Formulae and Earthwork 8vo, 

* Trautwine's Method of Calculating the Cube Contents of Excavations and 

Embankments by the Aid of Diagrams 8vo, 

The Field Practice of Laying Out Circular Curves for Railroads. 

i2mo, morocco, 

Cross-section Sheet Paper, 

Webb's Railroad Censtruction i6mo, morocco, 5 00 

Wellington's Economic Theory of the Location of Railways Small 8vo, 5 00 



DRAWING. 

Barr's Kinematics of Machinery 8vo, : 

* Bartlett's Mechanical Drawing 8vo, ; 

* " " " Abridged Ed 8vo, : 

Coolidge's Manual of Drawing 8vo, papejr : 

Coolidge and Freeman's Elements of General Drafting for Mechanical Engi- 
neers Oblong 4to, : 

Durley's Kinematics of Machines 8vo, , 

Emch's Introduction to Projective Geometry and its Applications 8vo, : 

Hill's Text-book on Shades and Shadows, and Perspective 8vo, 

Jamison's Elements of Mechanical Drawing 8vo, 

Advanced Mechanical Drawing 8vo, 

Jones's Machine Design : 

Part I. Kinematics of Machinery 8vo, 

Part n. Form, Strength, and Proportions of Parts 8vo, 

MacCord's Elements of Descriptive Geometry 8vo, 

Kinematics; or, Practical Mechanism 8vo, 

Mechanical Drawing 4to, 

Velocity Diagrams 8vo, 

MacLeod's Descriptive Geometry Small 8vo, 

* Mahan's Descriptive Geometry and Stone-cutting 8vo, 

Industrial Drawing. (Thompson.) 8vo, 

Moyer's Descriptive Geometry 8vo, 

Reed's Topographical Drawing and Sketching 4to, 

Reid's Course in Mechanical Drawing 8vo, 

Text-book of Mechanical Drawing and Elementary Machine Design. 8vo, 

Robinson's Principles of Mechanism 8vo, 

Schwamb and Merrill's Elements of Mechanism 8vo, 

Smith's (R. S.) Manual of Topographical Drawing. (McMillan.) 8vo, 

Smith (A. W.) and Marx's Machine Design 8vo, 

Warren's Elements of Plane and Solid Free-hand Geometrical Drawing, nmo, 

Drafting Instruments and Operations i2mo, 

Manual of Elementary Projection Drawing i2mo, 

Manual of Elementary Problems in the Linear Perspective of Form and 

Shadow i2mo, 

Plane Problems in Elementary Geometry i2mo, 



Warren's Primary Geometry i2mo, 75 

Elements of Descriptive Geometry, Shadows, and Perspective 8vo, 3 50 

General Problems of Shades and Shadows 8vo, 3 00 

Elements of Machine Construction and Drawing 8vo, 7 50 

Problems, Theorems, and Examples in Descriptive Geometry 8vo, 2 50 

Weisbach's Kinematics [and Power of Transmission. (Hermann and 

Klein.) 8vo, 5 o 

Whelpley's Practical Instruction in the Art of Letter Engraving nmo, 2 00 

Wilson's (H. M.) Topographic Surveying 8vo, 3 50 

Wilson's (V. T.) Free-hand Perspective. .* 8vo, 2 50 

Wilson's (V. T.) Free-hand Lettering 8vo, 1 00 

Woolf's Elementary Course in Descriptive Geometry Large 8vo, 3 00 

ELECTRICITY AND PHYSICS. 

Anthony and Brackett's Text-book of Physics. (Magie.) Small 8vo, 3 oc- 

Anthony's Lecture-notes on the Theory of Electrical Measurements. . . .i2mo, 1 00 

Benjamin's History of Electricity 8vo, 3 00 

Voltaic Cell 8vo, 3 00 

Classen's Quantitative Chemical Analysis by Electrolysis. (Boltwood.).8vo, 3 00 

Crehore and Squier's Polarizing Photo-chronograph 8vo, 3 00 

Dawson's "Engineering" and Electric Traction Pocket-book. i6mo, morocco, 5 00 
Dolezalek's Theory of the Lead Accumulator (Storage Battery). (Von 

Ende.) nmo, 2 50 

Duhem's Thermodynamics and Chemistry. (Burgess.) 8vo, 4 00 

Flather's Dynamometers, and the Measurement of Power i2mo, 3 00 

Gilbert's De Magnete. (Mottelay.) 8vo, 2 50 

Hanchett's Alternating Currents Explained i2mo, 1 00 

Hering's Ready Reference Tables (Conversion Factors) i6mo, morocco, 2 50 

Holman's Precision of Measurements 8vo, 2 00 

Telescopic Mirror-scale Method, Adjustments, and Tests. .. .Large 8vo, 75 

Xinzbrunner's Testing of Continuous-current Machines 8vo, 2 00 

Landauer's Spectrum Analysis. (Tingle.) 8vo, 3 00 

Le Chatelier s High-temperature Measurements. (Boudouard — Burgess.) i2mo, 3 00 

Lob's Electrochemistry of Organic Compounds. (Lorenz.) 8vo, 3 00 

* Lyons'? Treatise on Electromagnetic Phenomena. Vols. I. and II. 8vo, each, 6 00 

* Michie's Elements of Wave Motion Relating to Sound and Light 8vo, 4 00 

Niaudet's Elementary Treatise on Electric Batteries. (Fishback.) i2mo, 2 50 

* Rosenberg's Electrical Engineering. (Haldane Gee — Kinzbrunner.). . .8vo, 1 50 

Ryan, Norris, and Hoxie's Electrical Machinery. Vol. 1 8vo, 2 50 

Thurston's Stationary Steam-engines 8vo, 2 50 

* Tillman's Elementary Lessons in Heat 8vo, 1 50 

Tory and Pitcher's Manual of Laboratory Physics Small 8vo, 2 00 

Ulke's Modern Electrolytic Copper Refining 8vo, 3 00 

LAW. 

* Davis's Elements of Law 8vo, 2 50 

* Treatise on the Military Law of United States 8vo, 7 00 

* Sheep, 7 50 

Manual for Courts-martial i6mo, morocco, 1 50 

Wait's Engineering and Architectural Jurisprudence 8vo, 6 00 

Sheep, 6 so 
Law of Operations Preliminary to Construction in Engineering and Archi- 
tecture 8vo 5 00 

Sheep, 5 50 

Law of Contracts 8vo, 3 00 

Winthrop's Abridgment of Military Law i2mo, 2 50. 

10 



MANUFACTURES. 

Bernadou's Smokeless Powder — Nitro-cellulose and Theory of the Cellulose 

Molecule i2mo, 2 50 

Bolland's Iron Founder i2mo, 2 50 

" The Iron Founder," Supplement i2mo, 2 50 

Encyclopedia of Founding and Dictionary of Foundry Terms Used in the 

Practice of Moulding i2mo, 3 00 

Eissler's Modern High Explosives 8vo, 4 00 

Effront's Enzymes and their Applications. (Prescott.) 8vo, 3 00 

Fitzgerald's Boston Machinist i2mo, 1 00 

Ford's Boiler Making for Boiler Makers i8mo, 1 00 

Hopkin's Oil-chemists' Handbook 8vo, 3 00 

Keep's Cast Iron 8vo, 2 50 

Leach's The Inspection and Analysis of Food with Special Reference to State 

Control Large 8vo, 7 50 

Matthews's The Textile Fibres 8vo, 3 50 

Metcalf 's Steel. A Manual for Steel-users i2mo, 2 00 

Metcalfe's Cost of Manufactures — And the Administration of Workshops. 8vo, 5 00 

Meyer's Modern Locomotive Construction 4to, 10 00 

Morse's Calculations used in Cane-sugar Factories i6mo, morocco, 1 50 

* Reisig's Guide to Piece-dyeing 8vo, 23 00 

Sabin's Industrial and Artistic Technology of Paints and Varnish 8vo, 3 00 

Smith's Press-working of Metals 8vo, 3 00 

Spalding's Hydraulic Cement i2mo, 2 00 

Spencer's Handbook for Chemists of Beet-sugar Houses i6mo, morocco, 3 00 

Handbook for Cane Sugar Manufacturers i6mo, morocco, 3 00 

Taylor and Thompson's Treatise on Concrete, Plain and Reinforced 8vo, 5 00 

Thurston's Manual of Steam-boilers, their Designs, Construction and Opera- 
tion 8vo, 5 00 

* Walke's Lectures on Explosives 8vo, 4 00 

Ware's Beet-sugar Manufacture and Refining Small 8vo, 4 00 

West's American Foundry Practice i2mo, 2 50 

Moulder's Text-book i2mo, 2 50 

Wolff's Windmill as a Prime Mover 8vo, 3 00 

Wood's Rustless Coatings : Corrosion and Electrolysis of Iron and Steel. .8vo, 4 00 



MATHEMATICS. 

Baker's Elliptic Functions 8vo, 1 50 

* Bass's Elements of Differential Calculus i2mo, 4 00 

Briggs's Elements of Plane Analytic Geometry i2mo, 1 00 

Compton's Manual of Logarithmic Computations i2mo, 1 50 

Davis's Introduction to the Logic of Algebra 8vo, i 50 

* Dickson's College Algebra Large i2mo, 1 50 

* Introduction to the Theory of Algebraic Equations Large nmo, 1 25 

Emch's Introduction to Projective Geometry and its Applications 8vo, 2 50 

Halsted's Elements of Geometry. 8vo, 1 75 

Elementary Synthetic Geometry , 8vo, 1 50 

Rational Geometry i2mo, 1 75 

* Johnson's (J. B.) Three-place Logarithmic Tables: Vest-pocket size. paper, 15 

100 copies for 5 00 

* Mounted on heavy cardboard, 8X 10 inches, 25 

10 copies for 2 00 

Johnson's (W. W.) Elementary Treatise on Differential Calculus. .Small 8vo, 3 00 

Johnson's (W. W.) Elementary Treatise on the Integral Calculus . Small 8vo, 1 50 
11 



Johnson's (W. W.) Curve Tracing in Cartesian Co-ordinates i2mo, 

Johnson's (W. W.) Treatise on Ordinary and Partial Differential Equations. 

Small 8vo, 
Johnson's (W. W.) Theory of Errors and the Method of Least Squares, nmo, 

* Johnson's (W. W.) Theoretical Mechanics nmo, 

Laplace's Philosophical Essay on Probabilities. (Truscott and Emory.) . nmo, 

* Ludlow and Bass. Elements of Trigonometry and Logarithmic and Other 

Tables 8vo, 

Trigonometry and Tables published separately Each, 

* Ludlow's Logarithmic and Trigonometric Tables 8vo, 

Mathematical Monographs. Edited by Mansfield Merriman and Robert 

S. Woodward Octavo, each 

No. i. History of Modern Mathematics, by David Eugene Smith. 
No. 2. Synthetic Projective Geometry, by George Bruce Halsted. 
No. 3. Determinants, by Laenas Gifford Weld. No. 4. Hyper- 
bolic Functions, by James McMahon. No. 5. Harmonic Func- 
tions, by William E. Byerly. No. 6. Grassmann's Space Analysis, 
hy Edward W. Hyde. No. 7. Probability and Theory of Errors, 
by Robert S. Woodward. No. 8. Vector Analysis and Quaternions, 
by Alexander Macfarlane. No. 9. Differential Equations, by 
William Woolsey Johnson. No. 10. The Solution of Equations, 
byl Mansfield Merriman. No. n. Functions of a Complex Variable, 
by Thomas S. Fiske. 

Maurer's Technical Mechanics 8vo, 

Merriman and Woodward's Higher Mathematics 8vo, 

Merriman's Method of Least Squares 8vo, 

Rice and Johnson's Elementary Treatise on the Differential Calculus. . Sm. 8vo, 

Differential and Integral Calculus. 2 vols, in one Small 8vo, 

Wood's Elements of Co-ordinate Geometry 8vo, 

Trigonometry: Analytical, Plane, and Spherical nmo, 



MECHANICAL ENGINEERING. 

MATERIALS OF ENGINEERING, STEAM-ENGINES AND BOILERS. 

Bacon's Forge Practice nmo, 

Baldwin's Steam Heating for Buildings ; nmo, 

Barr's Kinematics of Machinery 8vo, 

* Bartlett's Mechanical Drawing 8vo, 

* " " " Abridged Ed 8vo, 

Benjamin's Wrinkles and Recipes nmo, 

Carpenter's Experimental Engineering 8vo, 

Heating and Ventilating Buildings 8vo, 

Cary's Smoke Suppression in Plants using Bituminous Coal. (In Prepara- 

Clerk's Gas and Oil Engine Small 8vo, 

Coolidge's Manual of Drawing 8vo, paper, 

Coolidge and Freeman's Elements of General Drafting for Mechanical En- 
gineers Oblong 4to 

Cromwell's Treatise on Toothed Gearing nmo, 

Treatise on Belts and Pulleys nmo, 

Durley's Kinematics of Machines 8vo, 

Flather's Dynamometers and the Measurement of Power nmo, 

Rope Driving nmo, 

Gill's Gas and Fuel Analysis for Engineers nmo, 

Hall's Car Lubrication nmo, 

Hering's Ready Reference Tables (Conversion Factors) i6mo, 

12 



Hutton's The Gas Engine 8vo, 5 00 

Jamison's Mechanical Drawing 8vo, 2 50 

Jones's Machine Design: 

Part I. Kinematics of Machinery 8vo, 1 50 

Part II. Form, Strength, and Proportions of Parts 8vo, 3 00 

Kent's Mechanical Engineers' Pocket-book i6mo, morocco, 5 00 

Kerr's Power and Power Transmission 8vo, 2 00 

Leonard's Machine Shop, Tools, and Methods 8vo, 4 00 

* Lorenz's Modern Refrigerating Machinery. (Pope, Haven, and Dean.) . . 8vo, 4 00 

MacCord's Kinematics; or, Practical Mechanism 8vo, 5 00 

Mechanical Drawing 4to, 4 00 

Velocity Diagrams 8vo, 1 50 

MacFarland's Standard Reduction Factors for Gases 8vo, 1 50 

Mahan's Industrial Drawing. (Thompson.) 8vo, 3 50 

Poole's Calorific Power of Fuels 8vo, 3 00 

Jieid's Course in Mechanical Drawing • 8vo, 2 00 

Text-book of Mechanical Drawing and Elementary Machine Design . 8vo, 3 00 

Richard's Compressed Air nmo, 1 50 

Robinson's Principles of Mechanism 8vo, 3 00 

Schwamb and Merrill's Elements of Mechanism 8vo, 3 00 

Smith's (O.) Press-working of Metals 8vo, 3 00 

Smith (A. W.) and Marx's Machine Design 8vo, 3 00 

Thurston's Treatise on Friction and Lost Work in Machinery and Mill 

Work 8vo, 3 00 

Animal as a Machine and Prime Motor, and the Laws of Energetics . i2mo, 1 00 

Warren's Elements of Machine Construction and Drawing 8vo, 7 so 

Weisbach's Kinematics and the Power of Transmission. (Herrmann — 

Klein.) 8vo, 5 00 

Machinery of Transmission and Governors. (Herrmann — Klein.). .8vo, 5 00 

Wolff's Windmill as a Prime Mover 8vo, 3 00 

Wood's Turbines 8vo, 2 50 



MATERIALS OP ENGINEERING. 

* Bovey's Strength of Materials and Theory of Structures 8vo, 7 50 

Burr's Elasticity and Resistance of the Materials of Engineering. 6th Edition. 

Reset 8vo, 7 50 

Church's Mechanics of Engineering 8vo, 6 00 

* Greene's Structural Mechanics 8vo, 2 50 

Johnson's Materials of Construction 8vo, 6 00 

Keep's Cast Iron 8vo, 2 50 

Lanza's Applied Mechanics 8vo, 7 50 

Martens 's Handbook on Testing Materials. (Henning.) 8vo, 7 50 

Maurer's Technical Mechanics 8vo, 4 00 

Merriman's Mechanics of Materials 8vo, 5 00 

Strength of Materials nmo, 1 00 

Metcalf's Steel. A manual for Steel-users nmo, 2. 00 

Sabin's Industrial and Artistic Technology of Paints and Varnish 8vo, 3 00 

Smith's Materials of Machines i2mo, 1 00 

Thurston's Materials of Engineering 3 vols., 8vo, 8 00 

Part II. Iron and Steel 8vo, 3 50 

Part III. A Treatise on Brasses, Bronzes, and Other Alloys and their 

Constituents 8vo, 2 50 

Text-book of the Materials of Construction 8vo, 5 00 

Wood's (De V.) Treatise on the Resistance of Materials and an Appendix on 

the Preservation of Timber 8vo, 2 00 

13 



Wood's (De V.) Elements of Analytical Mechanics 8vo, 3 00 

Wood's (M. P.) Rustless Coatings: Corrosion and Electrolysis of Iron and 

Steel 8vo, 4 00 

STEAM-ENGINES AND BOILERS. 

Berry's Temperature-entropy Diagram i2mo,. 1 25 

Carnot's Reflections on the Motive Power of Heat. (Thurston.) i2mo, I 50 

Dawson's " Engineering" and Electric Traction Pocket-book. . . . i6mo, mor., 5 00 

Ford's Boiler Making for Boiler Makers i8mo, I 00 

Goss's Locomotive Sparks 8vo, 2 00 

Hemenway's Indicator Practice and Steam-engine Economy i2mo, 2 00 

Hutton's Mechanical Engineering of Power Plants 8vo, 5 00 

Heat and Heat-engines 8vo, 5 00 

Kent's Steam boiler Economy 8vo, 4 00 

Kneass's Practice and Theory of the Injector 8vo, 1 50 

MacCord's Slide-valves 8vo, 2 00 

Meyer's Modern Locomotive Construction 4to, 10 00 

Peabody's Manual of the Steam-engine Indicator nmo, 1 50 

Tables of the Properties of Saturated Steam and Other Vapors 8vo, 1 00. 

Thermodynamics of the Steam-engine and Other Heat-engines 8vo, 5 00 

Valve-gears for Steam-engines 8vo, 2 50 

Peabody and Miller's Steam-boilers 8vo, 4 00 

Pray's Twenty Years with the Indicator Large 8vo, 2 50 

Pupin's Thermodynamics of Reversible Cycles in Gases and Saturated Vapors. 

(Osterberg.) i2mo, 1 25 

Reagan's Locomotives: Simple Compound, and Electric nmo, 2 50 

Rontgen's Principles of Thermodynamics. (Du Bois.) 8vo, 5 00 

Sinclair's Locomotive Engine Running and Management i2mo, 2 oa 

Smart's Handbook of Engineering Laboratory Practice i2mo, 2 50. 

Snow's Steam-boiler Practice 8vo, 3 00 

Spangler's Valve-gears 8vo, 2 50 

Notes on Thermodynamics nmo, 1 oa 

Spangler, Greene, and Marshall's Elements of Steam-engineering 8vo, 3 00 

Thurston's Handy Tables ., 8vo, 1 50 

Manual of the Steam-engine 2 vols., 8vo, 10 00 

Part I. History, Structure, and Theory 8vo, 6 oa 

Part II. Design, Construction, and Operation 8vo, 6 oa 

Handbook of Engine and Boiler Trials, and the Use of the Indicator and 

the Prony Brake 8vo, 5 oa 

Stationary Steam-engines 8vo, 2 50- 

Steam-boiler Explosions in Theory and in Practice nmo, 1 50 

Manual of Steam-boilers, their Designs, Construction, and Operation 8vo, 5 oa 

Weisbach's Heat, Steam, and Steam-engines. (Du Bois.) 8vo, 5 00 

Whitham's Steam-engine Design 8vo, 5 00 

Wilson's Treatise on Steam-boilers. (Flather.) i6mo, 2 50 

Wood's Thermodynamics, Heat Motors, and Refrigerating Machines. . .8vo, 4 00 



MECHANICS AND MACHINERY. 

Barr's Kinematics of Machinery 8vo, 2 50 

* Bovey's Strength of Materials and Theory of Structures 8vo, 7 50 

Chase's The Art of Pattern-making i2mo, 2 50 

Church's Mechanics of Engineering 8vo, 6 00 

Notes and Examples in Mechanics 8vo, 2 00 

Compton's First Lessons in Metal-working i2mo, 1 50 

Compton and De Groodt's The Speed Lathe nmo, 1 50 

14 



Cromwell's Treatise on Toothed Gearing i2mo, i 50 

Treatise on Belts and Pulleys nmo, 1 50 

Dana's Text-book of Elementary Mechanics for Colleges and Schools. . umo, 1 50 

Dingey's Machinery Pattern Making i2mo, 2 00 

Dredge's Record of the Transportation Exhibits Building of the World's 

Columbian Exposition of 1893 4to half morocco, 5 00 

Du Bois's Elementary Principles of Mechanics : 

Vol. I. Kinematics 8vo, 3 50 

Vol. II. Statics 8vo, 4 00 

Mechanics of Engineering. Vol. I Small 4to, 7 50 

Vol. II Small 4to, 10 00 

Durley's Kinematics of Machines 8vo, 4 00 

Fitzgerald's Boston Machinist i6mo, 1 00 

Flather's Dynamometers, and the Measurement of Power i2mo, 3 00 

Rope Driving i2mo, 2 00 

Goss's Locomotive Sparks 8vo, 2 00 

* Greene's Structural Mechanics 8vo, 2 50 

Hall's Car Lubrication i2mo, 1 00 

Holly's Art of Saw Filing i8mo, 75 

James's Kinematics of a Point and the Rational Mechanics of a Particle. 

Small 8vo, 2 00 

* Johnson's (W. W.) Theoretical Mechanics nmo, 3 00 

Johnson's (L. J.) Statics by Graphic and Algebraic Methods 8vo, 2 00 

Jones's Machine Design: 

Part I. Kinematics of Machinery 8vo, 1 50 

Part II. Form, Strength, and Proportions of Parts 8vo, 3 00 

Kerr's Power and Power Transmission 8vo, 2 00 

Lanza's Applied Mechanics 8vo, 7 50 

Leonard's Machine Shop, Tools, and Methods 8vo, 4 00 

* Lorenz's Modern Refrigerating Machinery. (Pope, Haven, and Dean.). 8vo, 4 00 
MacCord'* Kinematics; or, Practical Mechanism 8vo, 5 00 

Velocity Diagrams 8vo, 1 50 

Maurer's Technical Mechanics 8vo, 4 00 

Merriman's Mechanics of Materials 8vo, 5 00 

* Elements of Mechanics nmo, 1 00 

* Michie's Elements of Analytical Mechanics 8vo, 4 00 

Reagan's Locomotives: Simple, Compound, and Electric i2mo, 2 50 

Reid's Course in Mechanical Drawing 8vo, 2 00 

Text-book of Mechanical Drawing and Elementary Machine Design. 8vo, 3 00 

Richards's Compressed Air i2mo, 1 50 

Robinson's Principles of Mechanism 8vo, 3 00 

Ryan, Norris, and Hoxie's Electrical Machinery. Vol. 1 8vo, 2 50 

Schwamb and Merrill's Elements of Mechanism 8vo, 3 00 

Sinclair's Locomotive-engine Running and Management i2mo, 2 00 

Smith's (O.) Press-working of Metals 8vo, 3 00 

Smith's (A. W.) Materials of Machines nmo, 1 00 

Smith (A. W.) and Marx's Machine Design 8vo, 3 00 

Spangler, Greene, and Marshall's Elements of Steam-engineering 8vo, 3 00 

Thurston's Treatise on Friction and Lost Work in Machinery and Mill 

Work 8vo, 3 00 

Animal as a Machine and Prime Motor, and the Laws of Energetics. 

nmo, 1 00 

Warren's Elements of Machine Construction and Drawing 8vo, 7 50 

Weisbach's Kinematics and Power of Transmission. (Herrmann — Klein. ).8vo, 5 00 

Machinery of Transmission and Governors. (Herrmann — Klein. ).8vo, 5 00 

Wood's Elements of Analytical Mechanics 8vo, 3 00 

Principles of Elementary Mechanics nmo, 1 25 

Turbines 8vo, 2 50 

The World's Columbian Exposition of 1893 4to, 1 00 

15 



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METALLURGY. 

Egleston's Metallurgy of Silver, Gold, and Mercury: 

Vol. I. Silver 8vo, 

Vol. II. Gold and Mercury 8vo, 

** Iles's Lead-smelting. (Postage o cents additional.) i2mo. 

Keep's Cast Iron 8vo 

Kunhardt's Practice of Ore Dressing in Europe 8vo ; 

Le Chatelier's High-temperature Measurements. (Boudouard — Burgess. )i2mo, 

Metcalf's Steel. A Manual for Steel-users i2mo, 

Minet's Production of Aluminum and its Industrial Use. (Waldo.). . . . nmo, 

Robine and Lenglen's Cyanide Industry. (Le Clerc.) 8vo, 

Smith's Materials of Machines i2mo, 

Thurston's Materials of Engineering. In Three Parts 8vo, 

Part II. Iron and Steel 8vo, 

Part III. A Treatise on Brasses, Bronzes, and Other Alloys and their 

Constituents 

Ulke's Modern Electrolytic Copper Refining 8vo, 



MINERALOGY. 

Barringer's Description of Minerals of Commercial Value. Oblong, morocco, 2 50 

Boyd's Resources of Southwest Virginia 8vo, 3 00 

Map of Southwest Virignia Pocket-book form. 2 00 

Brush's Manual of Determinative Mineralogy. (Penfield.) 8vo, 4 00 

Chester's Catalogue of Minerals 8vo, paper, 1 00 

Cloth, 1 25 

Dictionary of the Names of Minerals 8vo, 3 50 

Dana's System of Mineralogy Large 8vo, half leather, 12 50 

First Appendix to Dana's New " System of Mineralogy." Large 8vo, 1 00 

Text-book of Mineralogy 8vo, 4 00 

Minerals and How to Study Them nmo, 1 50 

Catalogue of American Localities of Minerals Large 8vo, 1 00 

Manual of Mineralogy and Petrography i2mo, 2 00 

Douglas's Untechnical Addresses on Technical Subjects i2mo, 1 00 

Eakle's Mineral Tables 8vo, 1 25 

Egleston's Catalogue of Minerals and Synonyms 8vo, 2 50 

Hussak's The Determination of Rock-forming Minerals. (Smith.). Small 8vo, 2 00 

Merrill's Non-metallic Minerals: Their Occurrence and Uses 8vo, 4 00 

* Penfield's Notes on Determinative Mineralogy and Record of Mineral Tests. 

8vo, paper, 50 
Rosenbusch's Microscopical Physiography of the Rock-making Minerals. 

(Iddings.) 8vo, 5 00 

* Tillman's Text-book of Important Minerals and Rocks 8vo, 2 00 



Beard's Ventilation of Mines i2mo, 2 50 

Boyd's Resources of Southwest Virginia 8vo, 3 00 

Map of Southwest Virginia Pocket-book form, 2 00 

Douglas's Untechnical Addresses on Technical Subjects i2mo, 1 00 

* Drinker's Tunneling, Explosive Compounds, and Rock Drills. .4to,hf. mor., 25 00 

Eissler's Modern High Explosives 8vo. 4 00 

16 



Fowler's Sewage Works Analyses i2mo. 

Goodyear's Coal-mines of the Western Coast of the United States i2mo ; 

Ihlseng's Manual of Mining 8vo. 

** lles's Lead-smelting. (Postage oc. additional.) i2mo. 

Kunhardt's Practice of Ore Dressing in Europe 8vo, 

O'Driscoll's Notes on the treatment of Gold Ores 8vo. 

Robine and Lenglen's Cyanide Industry. (Le Clerc.) 

* Walke's Lectures on Explosives , 

Wilson's Cyanide Processes i2mo ( 

Chlorination Process i2mo. 

Hydraulic and Placer Mining i: 

Treatise on Practical and Theoretical Mine Ventilation T2mo, 



SANITARY SCIENCE. 

Bashore's Sanitation of a Country House i2mo, i oo 

Folwell's Sewerage. (Designing, Construction, and Maintenance.) 8vo, 3 00 

Water-supply Engineering 8vo, 4 00 

Fuertes's Water and Public Health i2mo, 1 50 

Water-filtration Works i2mo, 2 50 

Gerhard's Guide to Sanitary House-inspection i6mo, 1 00 

Goodrich's Economic Disposal of Town's Refuse Demy 8vo, 3 50 

Hazen's Filtration of Public Water-supplies 8vo, 3 00 

Leach's The Inspection and Analysis of Food with Special Reference to State 

Control 8vo, 7 50 

Mason's Water-supply. (Considered principally from a Sanitary Standpoint) 8vo, 4 00 

Examination of Water. (Chemical and Bacteriological.) i2mo, 1 25 

Ogden's Sewer Design i2mo, 2 00 

Prescott and Winslow's Elements of Water Bacteriology, with Special Refer- 
ence to Sanitary Water Analysis " i2mo, 1 25 

* Price's Handbook on Sanitation i2mo, j 50 

Richards's Cost of Food. A Study in Dietaries. i2mo, 1 00 

Cost of Living as Modified by Sanitary Science nmo, 1 00 

Richards and Woodman's Air. Water, and Food from a Sanitary Stand- 
point 8vo, 2 00 

* Richards and Williams's The Dietary Computer 8vo, 1 50 

Rideal's Sewage and Bacterial Purification of Sewage .8vo, 3 50 

Turneaure and Russell's Public Water-supplies 8vo, 5 00 

Von Behring's Suppression of Tuberculosis. (Bolduan.) i2mo, 1 00 

Whipple's Microscopy of Drinking-water 8vo, 3 50 

Winton's Microscopy of Vegetable Foods 8vo, 7 50 

Woadhull's Notes on Military Hygiene i6mo, 1 50 



MISCELLANEOUS. 

De Fursac's Manual of Psychiatry. (Rosanoff and Collins.). . . .Large i2mo, 
Emmons's Geological Guide-book of the Rocky Mountain Excursion of the 

International Congress of Geologists Large 8vo, 

Ferrel's Popular Treatise on the Winds , 8vo. 

Haines's American Railway Management i2mo, 

Mott's Fallacy of the Present Theory of Sound i6mo, 

Ricketts's History of Rensselaer Polytechnic Institute, 1824-1894. .Small 8vo, 

Rostoski's.Serum Diagnosis. (Bolduan.) i2mo, 

Rotherham's Emphasized New Testament Large 8vo, 

17 



Steel's Treatise on the Diseases of the Dog 8vo, 3 50 

The World's Columbian Exposition of 1893 4to, 1 00 

Von Behring's Suppression of Tuberculosis. (Bolduan.) nmo, 1 00 

Winslow's Elements of Applied Microscopy nmo, 1 50 

Worcester and Atkinson. Small Hospitals, Establishment and Maintenance; 

Suggestions for Hospital Architecture: Plans for Small Hospital. i2mo, 1 25 



HEBREW AND CHALDEE TEXT-BOOKS. 

Green's Elementary Hebrew Grammar i2mo, 

Hebrew Chrestomathy 8vo, 

Gesenius's Hebrew and Chaldee Lexicon to the Old Testament Scriptures. 

(Tregelles.) Small 4to, half morocco, 

Letteris's Hebrew Bible 8vo, 

18 



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